Circles
Central, inscribed and circumscribed angles
None
Watch the entire video
Inscribed and central angles
Showing that an inscribed angle is half of a central angle that subtends the same arc
Discussion and questions for this video
Do you understand English? Click here to see more discussion happening on Khan Academy's English site.
 What I want to do in this video is to prove one of the more
 useful results in geometry, and that's that an inscribed angle
 is just an angle who's vertex sits on the circumference
 of the circle.
 So that is our inscribed angle.
 I'll denote it by si  I'll use the si for inscribed angle
 and angles in this video.
 That si, the inscribed angle, is going to be exactly 1/2 of
 the central angle that subtends the same arc.
 So I just used a lot a fancy words, but I think you'll
 get what I'm saying.
 So this is si.
 It is an inscribed angle.
 It sits, it's vertex sits on the circumference.
 And if you draw out the to rays that come out from this angle
 or the two cords that define this angle, it intersects the
 circle at the other end.
 And if you look at the part of the circumference of the circle
 that's inside of it, that is the arc that is
 subtended by si.
 It's all very fancy words, but I think the idea is
 pretty straightforward.
 This right here is the arc subtended by si, where si is
 that inscribed angle right over there, the vertex sitting
 on the circumference.
 Now, a central angle is an angle where the vertex is
 sitting at the center of the circle.
 So let's say that this right here  I'll try to eyeball
 it  that right there is the center of the circle.
 So let me draw a central angle that subtends this same arc.
 So that looks like a central angle subtending that same arc.
 Just like that.
 Let's call this theta.
 So this angle is si, this angle right here is theta.
 When I'm going to prove in this video is that si is always
 going to be equal to 1/2 of theta.
 So if I were to tell you that si is equal to, I don't know,
 25 degrees, then you would immediately know that theta
 must be equal to 50 degrees.
 Or if I told you that theta was 80 degrees, then you would
 immediately know that si was 40 degrees.
 So let's actually proved this.
 So let me clear this.
 So a good place to start, or the place I'm going to
 start, is a special case.
 I'm going to draw a inscribed angle, but one of the cords
 that define it is going to be the diameter of the circle.
 So this isn't going to be the general case, this is going
 to be a special case.
 So let me see, this is the center right here of my circle.
 I'm trying to eyeball it.
 Center looks like that.
 So let me draw a diameter.
 So the diameter looks like that.
 Then let me define my inscribed angle.
 This diameter is one side of it.
 And then the other side maybe is just like that.
 So let me call this right here si.
 If that's si, this length right here is a radius  that's
 our radius of our circle.
 Then this length right here is also going to be the radius of
 our circle going from the center to the circumference.
 Your circumference is defined by all of the points that are
 exactly a radius away from the center.
 So that's also a radius.
 Now, this triangle right here is an isosceles triangle.
 It has two sides that are equal.
 Two sides that are definitely equal.
 We know that when we have two sides being equal, their
 base angles are also equal.
 So this will also be equal to si.
 You might not recognize it because it's
 tilted up like that.
 But I think many of us when we see a triangle that looks like
 this, if I told you this is r and that is r, that these two
 sides are equal, and if this is si, then you would also
 know that this angle is also going to be si.
 Base angles are equivalent on an isosceles triangle.
 So this is si, that is also si.
 Now, let me look at the central angle.
 This is the central angle subtending the same arc.
 Let's highlight the arc that they're both subtending.
 This right here is the arc that they're both going to subtend.
 So this is my central angle right there, theta.
 Now if this angle is theta, what's this angle going to be?
 This angle right here.
 Well, this angle is supplementary to theta,
 so it's 180 minus theta.
 When you add these two angles together you go 180 degrees
 around or the kind of formal line.
 They're supplementary to each other.
 Now we also know that these three angles are sitting
 inside of the same triangle.
 So they must add up to 180 degrees.
 So we get si  this si plus that si plus si plus this
 angle, which is 180 minus theta plus 180 minus theta.
 These three angles must add up to 180 degrees.
 They're the three angles of a triangle.
 Now we could subtract 180 from both sides.
 Si plus si is 2 si minus theta is equal to 0.
 Add theta to both sides.
 You get 2 si is equal to theta.
 Multiply both sides by 1/2 or divide both sides by 2.
 You get si is equal to 1/2 of theta.
 So we just proved what we set out to prove for the special
 case where our inscribed angle is defined, where one on the
 rays, if you want to view these lines as rays, where one of the
 rays that defines this inscribed angle is
 along the diameter.
 The diameter forms part of that ray.
 So this is a special case where one edge is
 sitting on the diameter.
 So already we could generalize this.
 So now that we know that if this is 50 that this is
 going to be 100 degrees and likewise, right?
 Whatever si is or whatever theta is, si's going to be 1/2
 of that, or whatever si is, theta is going to
 be 2 times that.
 And now this will apply for any time.
 We could use this notion any time that  so just using that
 result we just got, we can now generalize it a little bit,
 although this won't apply to all inscribed angles.
 Let's have an inscribed angle that looks like this.
 So this situation, the center, you can kind of view it as
 it's inside of the angle.
 That's my inscribed angle.
 And I want to find a relationship between this
 inscribed angle and the central angle that's subtending
 to same arc.
 So that's my central angle subtending the same arc.
 Well, you might say, hey, gee, none of these ends or these
 cords that define this angle, neither of these are diameters,
 but what we can do is we can draw a diameter.
 If the center is within these two cords we
 can draw a diameter.
 We can draw a diameter just like that.
 If we draw a diameter just like that, if we define this angle
 as si 1, that angle as si 2.
 Clearly si is the sum of those two angles.
 And we call this angle theta 1, and this angle theta 2.
 We immediately you know that, just using the result I just
 got, since we have one side of our angles in both cases being
 a diameter now, we know that si 1 is going to be
 equal to 1/2 theta 1.
 And we know that si 2 is going to be 1/2 theta 2.
 Si 2 is going to be 1/2 theta 2.
 So si, which is si 1 plus si 2, so si 1 plus si 2 is going to
 be equal to these two things.
 1/2 theta 1 plus 1/2 theta 2.
 Si 1 plus si 2, this is equal to the first inscribed
 angle that we want to deal with, just regular si.
 That's si.
 And this right here, this is equal to 1/2 times
 theta 1 plus theta 2.
 What's theta 1 plus theta 2?
 Well that's just our original theta that
 we were dealing with.
 So now we see that si is equal to 1/2 theta.
 So now we've proved it for a slightly more general case
 where our center is inside of the two rays that
 define that angle.
 Now, we still haven't addressed a slightly harder situation or
 a more general situation where if this is the center of our
 circle and I have an inscribed angle where the center isn't
 sitting inside of the two cords.
 Let me draw that.
 So that's going to be my vertex, and I'll switch colors,
 so let's say that is one of the cords that defines the
 angle, just like that.
 And let's say that is the other cord that defines
 the angle just like that.
 So how do we find the relationship between, let's
 call, this angle right here, let's call it si 1.
 How do we find the relationship between si 1 and the central
 angle that subtends this same arc?
 So when I talk about the same arc, that's that right there.
 So the central angle that subtends the same arc
 will look like this.
 Let's call that theta 1.
 What we can do is use what we just learned when one side of
 our inscribed angle is a diameter.
 So let's construct that.
 So let me draw a diameter here.
 The result we want still is that this should be 1/2 of
 this, but let's prove it.
 Let's draw a diameter just like that.
 Let me call this angle right here, let me call that si 2.
 And it is subtending this arc right there  let me do
 that in a darker color.
 It is subtending this arc right there.
 So the central angle that subtends that same arc,
 let me call that theta 2.
 Now, we know from the earlier part of this video that si
 2 is going to be equal to 1/2 theta 2, right?
 They share  the diameter is right there.
 The diameter is one of the cords that forms the angle.
 So si 2 is going to be equal to 1/2 theta 2.
 This is exactly what we've been doing in the last video, right?
 This is an inscribed angle.
 One of the cords that define is sitting on the diameter.
 So this is going to be 1/2 of this angle, of the central
 angle that subtends the same arc.
 Now, let's look at this larger angle.
 This larger angle right here.
 Si 1 plus si 2.
 Right, that larger angle is si 1 plus si 2.
 Once again, this subtends this entire arc right here, and it
 has a diameter as one of the cords that defines
 this huge angle.
 So this is going to be 1/2 of the central angle that
 subtends the same arc.
 We're just using what we've already shown in this video.
 So this is going to be equal to 1/2 of this huge central angle
 of theta 1 plus theta 2.
 So far we've just used everything that we've learned
 earlier in this video.
 Now, we already know that si 2 is equal to 1/2 theta 2.
 So let me make that substitution.
 This is equal to that.
 So we can say that si 1 plus  instead of si 2 I'll write
 1/2 theta 2 is equal to 1/2 theta 1 plus 1/2 theta 2.
 We can subtract 1/2 theta 2 from both sides, and
 we get our result.
 Si 1 is equal to 1/2 theta one.
 And now we're done.
 We have proven the situation that the inscribed angle is
 always 1/2 of the central angle that subtends the same arc,
 regardless of whether the center of the circle is inside
 of the angle, outside of the angle, whether we have a
 diameter on one side.
 So any other angle can be constructed as a sum of
 any or all of these that we've already done.
 So hopefully you found this useful and now we can actually
 build on this result to do some more interesting
 geometry proofs.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
how would it be use for this equation for an acual problem? i remember things applied in real situation.
Optics, Electromagnetic Radiation, & Gravity.
There are a host of phenomena in physics that vary with distance in a manner which is proportional to the inverse of the square of the distance.
If you were to measure the diameter of the sun when viewed at a distance, and were then to double that distance the observed diameter would be one half that of the original observation. Because the observed surface area of the suns disk is related to its radius which varies in the same manner, the surface area of the image will be 1/4 of the original image. To be more explicit A=Pi*r^2, and so if you substitute (1/2)r for r you will find that A=(1/4)*Pi*r^2. It turns out this result can be generalized and so is applicable to all distances. This notion also is implicit in perspective drawings and in optical phenomena. Hold your hand one foot from your eye, and then increase the distance to two feet. The size of the image of your hand in your visual field is owing to the angle subtended.
The gravitational force between two objects also varies in this manner. Hence the formula F=G(m1*m2)/R^2 where R=distance between two objects.
So yeah, this is actually something that many people find both interesting and useful. To understand all sorts of physics and engineering topics an understanding geometry is needed. The lecture that Sal gave is a part of this body of knowledge.
It might also be said that geometry is "a real situation."
There are a host of phenomena in physics that vary with distance in a manner which is proportional to the inverse of the square of the distance.
If you were to measure the diameter of the sun when viewed at a distance, and were then to double that distance the observed diameter would be one half that of the original observation. Because the observed surface area of the suns disk is related to its radius which varies in the same manner, the surface area of the image will be 1/4 of the original image. To be more explicit A=Pi*r^2, and so if you substitute (1/2)r for r you will find that A=(1/4)*Pi*r^2. It turns out this result can be generalized and so is applicable to all distances. This notion also is implicit in perspective drawings and in optical phenomena. Hold your hand one foot from your eye, and then increase the distance to two feet. The size of the image of your hand in your visual field is owing to the angle subtended.
The gravitational force between two objects also varies in this manner. Hence the formula F=G(m1*m2)/R^2 where R=distance between two objects.
So yeah, this is actually something that many people find both interesting and useful. To understand all sorts of physics and engineering topics an understanding geometry is needed. The lecture that Sal gave is a part of this body of knowledge.
It might also be said that geometry is "a real situation."
^up one best explanation by far
@ King.Classroom :D you made my day!
Probably the most relevant area of "real world" application is triangulation of location. Ie, to locate yourself on a phone with GPS you need to triangulate multiple distances (each of which defines the arc of a circle), and determine intersections. The rule in particular might not be relevant, but the type of geometric logic being used here certainly is critical.
Math competitions like the AMC12 or Putnam exam + a wide variety of applications in economics & physics.
Wow! Thank you Davidecheverria17 for sparking this fascinating thread.
what is a putnam square
cansome one like this comment
These r properties that we learn about. Later in calculus and engineering u will probably use these properties.
what is sy and data?
Psi and theta are Greek letters. Here psi is used to represent the unknown value of the inscribed angle. Theta is used to represent the unknown value of the central angle. Greek letters are often used to represent unknown angles in geometry like x, y and z are used to represent the unknown in algebra.
oh thank you!
Both are Greek symbol letters, and are almost like variables. They are used a lot in these types of problems. Check out the links to the wikipedia on these topics:
Psi: http://en.wikipedia.org/wiki/Psi
Theta: http://en.wikipedia.org/wiki/Theta
Psi: http://en.wikipedia.org/wiki/Psi
Theta: http://en.wikipedia.org/wiki/Theta
PSY is a Korean music artist known for his songs "Gangnam Style" and "Gentleman" and data is a term for information used usually in context with computers and the internet.
But you are probobly wondering about PSI (Ψ) and THETA (θ) which are the 23 and eighth letters in the greek alphabet, respectively. Sal sometimes uses them as variables, instead of x or y or whatever.
But you are probobly wondering about PSI (Ψ) and THETA (θ) which are the 23 and eighth letters in the greek alphabet, respectively. Sal sometimes uses them as variables, instead of x or y or whatever.
not DATA, THETA (at first I thought it was Beta). Psi and Theta are Greek letters (ψ and ϴ).
Psi and Theta are greek letters that in this case are being used as angle labels.
Psi and Theta are Greek symbol lettters
That are Greek letters.
At 0:25, is there a special meaning si has? Oh, and theta too. (2:01.)
psi and theta are just like using x in algebra they are just variables
I'm pretty sure it's just to distinguish them as angles rather than lengths, so you can have both in a picture at the same time and it will be a bit less confusing. And it's Greek as opposed to another language because it's the Greeks who did all this geometry in the beginning.
Thanks, and I also found this out: psi and theta are both greek letters, not to mention pi and tau! Does anyone know WHY greek letters are often used as variables in geometery?
No it is just a common variable used in Geometry class, sort'a!
psi and theta are merely just variables, they are virtually the same as using x or y in algebra.
Good question
Good question
Ever notice that theta is a circle with a ruler going though it..and psi is half a circle with a ruler going though it...staying true to the measure in the symbolism.
They are just Latin word's which are used as variable's or to denote something.
At 8:22 how do you know psi 1 is = to 1/2 beta 1, and same for psi 2 and beta 2?
At 6:00 minutes of this video Sal proves psi = 1/2 beta when one ray is a diameter, in the example you're asking about he creates a diameter so he can use this result to know Psi 1 = 1/2 beta 1 and the same for psi 2 and beta 2.
it's Theta, not beta.
ah I see ok thanks!
This (θ) is Theta and here's a funny emoticon that uses it: (>O<)θ (>o<)~✩
at 00:38 you mentioned si for the first time. What does si signify?
Psi (ψ) (not si) is a Greek letter. It's just a variable, like theta (θ). He's using it because there are two important angles so he needs a different letter for each.
It's a Greek letter...
Could you do a problem like this with different variables?
Like, instead of Psi and Theta, could you use x and y?
Like, instead of Psi and Theta, could you use x and y?
Yes, you can use whichever variables you like. But x and y are commonly used to indicate lengths, and psi and theta are commonly used to indicate angles, so that's what Sal has done.
I had a question about theta. If someone draws the symbol theta would you draw the line that goes in the center only as long as the radus or to the diameter? Thank you very much.
Theta is simply a variable that he uses to describe one of the two types of angles used in the above video: central angles. The symbol theta has no meaning specific to the concept discussed in the above video; like Psi, which he uses to indicate the inscribed angles, the Theta symbol is used to represent something, therefore it is not how the symbol is drawn that mattersit is what the symbol represents that matters.
The line in symbol theta goes through the diameter:θ Hope that helps! Plz vote up...
At 0:11 and 0:45, Sal says "vertex", what does that mean?
The Vertex is the point where the two line segments meet. So at 00:11 when he points to the vertex he is staying, the place where the two line segments meet, which is on the circumference of the circle
A vertex is when two lines connect and the corner is the vertex
A vertex is the point at which two line segments, rays, or lines intersect, forming an angle.
Can the rays of Si be outside of the circle and not inside?
The answer is yes. The rays forming si can intersect outside the circle. In this case, the the angle will sustend two arcs on the circle. The measure of angle si will then be 1/2(arc2  arc1). Arc2 being the larger arc and Arc1 being the smaller arc.
not si, psi. Like in pteranadon, it has a silent P.
Your answer is yes.
Your answer is yes.
Wait, in that third situation, what garuntee do you have that si 2 = theta 2? There are three triangles in that part of the video (at 11:25) and in the other parts, then there are two triangles? It doesn't really make much sense.
he's taking from the first example if one of the chords of the angle is the diameter then we already know that psi= 1/2theta, we already proved that. so using that we know that psi2=½(theta2) and we can and since the huge angle we made also has one of the chords on the diameter, we can state that psi1+psi2=½(theta1+theta2). Since we know that psi2=1/2theta1, we can plug it in and now we have psi1+1/2theta1=½theta1 +½ theta2 and the term 1/2theta1 cancels from both sides and you are left with psi1=1/2theta1, which are the two measurements we were looking for.Hope this helps.
At 10:05 What is "si"?
Actually, it is Psi, don't do Psy because he is a Kpop star.
Psi is a Greek letter used to represent an unknown value of a angle formed by 2 chords which have a common endpoint. (A inscribed angle)
Psi is a Greek letter used to represent an unknown value of a angle formed by 2 chords which have a common endpoint. (A inscribed angle)
That is the Greek letter Psy, or Ψ.
I don't get it... why not just use X or Z?
Because X and Z are for algebra. psi (but the p is silent) and theta. They're just variable traditionally used for angles( they are Greek letters)
at about 02:00, Sal talks about theta, and at about 00:38, he talks about psi. What do these mean?
Theta and Psi are letters in the Greek alphabet. They are commonly used to represent angles, the same way letters like a, b, c, or x, y, or z are commonly used as variables to represent unknowns in algebraic expressions. He could have used any letter to represent the angles. Hope this helps. Good Luck.
A plane is a flat surface with a thickness of 0. Any three points not on the same line will make a plane.
what's psi annd what are its uses ?
Although the definition for p.s.i above is correct, what is used in the video is Psi, a Greek letter. It is used to represent an unknown angle, like a more traditional x or y.
i agree with chrissy
Pounds per Square Inch.
It is a unit of pressure. Next time you fill your tires with air look for that acronym on the side of the tire. It tells you the correct pressure you should fill your tires.
It is a unit of pressure. Next time you fill your tires with air look for that acronym on the side of the tire. It tells you the correct pressure you should fill your tires.
What grade math is this?
Geometry can be taken in 8th grade, I don't think any 7th graders take it but maybe, and of course any high schooler can take it, 912th, but its usually 10th grade (:
Usually 8th graders take a very basic course of this. Tenth grade is when you actually take this full course in detail and it is required for graduation. If you take it in eight grade, it doesn't count towards your graduation unless you under special circumstances.
how does he know psi 1 equal 1/2 theta 1 at 8:15 in the vidio? i didn't undrstand the proof. i don't think i saw a proof. like wise for scy 2 and thaita 2 at 8:20
Sal wasnt really proving anything in particular. All he wanted to show was that the centre neednt be within the arc being subtended.
And he just did that using stuff that he had taught before
And he just did that using stuff that he had taught before
He clearly shows that an inscribed angle is one half of the central angle that subtends the same arc but does that mean that it is one half of the arc that it subtends as well?For example if an arc is 90 degrees does that mean that the inscribed angle subtended by that arc is 45 degrees?
I think that when you're measuring an arc in degrees, you're basically finding the central angle. So if I understood both questions correctly, it's both yes.
Are Psi and Theta used as placeholder for a value?
Yes. Just like x and y, they stand in for a value you don't know at the moment or else as a variable that might change. θ and ψ are nearly always used to represent angles, while x and y are used for points, lines, and curves.
For reference sake, just as x is the standard variable to use for an unknown, and if you need a second one it is standard to use y; with angles it is standard to use θ as the first unknown angle's variable and ψ for the second unknown angle. However, some people (myself included) tend to use α and β after having used θ.
But, really, it is all just arbitrary placeholders. You can call it anything you like, but math teachers tend to like for you to stick to traditional variables.
For reference sake, just as x is the standard variable to use for an unknown, and if you need a second one it is standard to use y; with angles it is standard to use θ as the first unknown angle's variable and ψ for the second unknown angle. However, some people (myself included) tend to use α and β after having used θ.
But, really, it is all just arbitrary placeholders. You can call it anything you like, but math teachers tend to like for you to stick to traditional variables.
Why doesn't the question page show up? I can't see the answer to my own question!
Go to your profile and click on discussion to see questions you've asked and answers you've given. There's a lot of people on here, so it can be hard to find yourself without that.
Since si is an inscribed circle and theta is the central angle that subtends the same arc as si, shouldn't theta be 2 times si and not 1/2 of si?
why psi and theta instead of a or b? Do they stand for something or are they just variables?
What does Sai or Si, whatever you call it, mean?
do you mean psi?
if so, its a Greek letter used to denote angles
if so, its a Greek letter used to denote angles
what? what are you talking about. be more specific. I might be able to help you :)
You have explained this much better than my teacher! Can you please make more geometry videos. Especially using the Common Core.
What does Subtended mean at 1:32
It's the amount of arc that's 'cut out' by the two lines extended from the angle we're talking about.  that should be clear from the vid @1:32
Is Si a mathematical expression like theta or is it representing a number?
It is spelt Psi. See http://en.wikipedia.org/wiki/Psi_(letter). It is a greek letter, like alpha, beta, gamma, pi. For a full list of greek letters and how they're used in mathematics and science see http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering. Sal could've picked another letter if he wanted. Perhaps he wanted to have a change for this video.
If the interior angles of a circle add up to 360 degrees, then what about an ellipse? Would the angles of an ellipse add up to 360 degrees as well?
Yes. You know how all squares are rectangles, but not all rectangles are squares? The same is true for circles. All circles are ellipses, but not all ellipses are circles.
Since a circle is just a special ellipse, then if a circle = 360, then so does an ellipse.
Since a circle is just a special ellipse, then if a circle = 360, then so does an ellipse.
I have always wondered is it Theta or Beta?
Theta and Beta are just traditionally used variables for angles.
College Board Sat Official Practice Test Question: #8. Square RSTU is inscribe in the circle. What is the degree measure of arc ST?
can i get a credit for watching these video taking notes
what does si mean or stand for? i dont get it:(
psi is a greek character, he's just using it to denote the angle.
HEY guys(gals) I have a question... what is the meaning of si(the pitchfork looking thing) and beta? (the circle with the line through it?)
Psi and theta are Greek letters. They are used many times as variables for unknown angles.
Use this link to find out what they mean  http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,
Is si/psi spelled si or psi? I've seen both spellings this video.
It is spelled "Psi" and the sign Ψ is the 23 letter of the greek alphabet which means Ps
What is subtending?
Subtending of an angle is the angle created when two lines intersect in a circle at the center.
It's "theta". It is a Greek letter that is used mostly to represent unknown angles.
how to find lettered angles in a circle?
The lettered angles are just variables, like x or y. Think nothing differently of them then you would if you were dealing with a regular a,b,c variable.
is SI a greek character??
yes and it's psi not si. =)
Why does Sal use psi? What is the purpose of Psi? I dont use psi and i also didnt know what it was.
It is standard practice in mathematics to use Greek letters to represent angles. Among the more commonly used are θ, ψ, φ , α, β, γ (Theta, psi, phi, alpha, beta, and gamma). Sometimes you'll see people use omega (ω).
It would be a good idea to learn the Greek alphabet. You don't necessarily need to know the names of all the letters, but just be able to recognize and draw them (though I would recommend learning the names of the more commonly used Greek letters)
It would be a good idea to learn the Greek alphabet. You don't necessarily need to know the names of all the letters, but just be able to recognize and draw them (though I would recommend learning the names of the more commonly used Greek letters)
okay this is a good video but my school isn't learning si or data so now I'm even more confused what do they stand for?
Psi and Theta are just variables like "x" and "y" that stand for angles. They are greek letters.
Psi looks like this Ψ and Theta looks like this Θ. They are both part of the greek alphabet.Ψ means PS and Θ means TH
what does subtending mean?
Subtending an arc means that the arms of the angle are separating a part of the circle. They are creating a new arc of the circle.
It basically is saying that there are two (or more) angles whose arms end in the same place.
It basically is saying that there are two (or more) angles whose arms end in the same place.
how does sal gets 1/2 at 5:50  5:56
He divided both sides of the equation by 2.
i.e. if 2 pens are worth 1 dollar, then 1 pen is worth 1/2 a dollar.
i.e. if 2 pens are worth 1 dollar, then 1 pen is worth 1/2 a dollar.
What is the biggest and smallest possible angle
Technically, the smallest angle could be 0 degrees, and the largest, 360. But, with both of those the angle is practically either ending, or just beginning, and is really nonexistent. So, the smallest angle possible would be 1 degree large (or a decimal value of that, such as 0.000001), and the largest angle would be 359 (or again, a decimal value, such as 359.99999). Any smaller or larger (depending on what we are considering) and the angle starts all over again, or becomes nothing at all. Does that make sense?
find RVT if <RST is a central angle of circle S.
S = 118
S = 118
RST is because if the circle is called circle S, than <S = <RST.
what are these ideas useful for?
Hey sal, could you please make a video about cyclic quadrilaterals? thanks :)
Does 'subtend' just mean that it goes through an arc of the circle?
am i spelling this right?: si and data
Why is it the only actual number I see in this entire video is 180? Don't the other angles have to be numbers?
I've only watched this video five times now. Having trouble conceptualizing this.
I've only watched this video five times now. Having trouble conceptualizing this.
its all unknowns the only thing you know for sure is that the angle of a straight line is 180. the ffigures are only there to help, they dont show the actual angle, therefore they are represented by variables. in geometry, greek letters are used as variables just as english letters are used in algebra. Yes, the other angles have to be numbers, but we dont know exactly what numbers they are.
In Trigonometry, Theta and Si are used, not x and y;
I do not understand either, actually!
I do not understand either, actually!
Thanks, but that just leads to another question: why not use x and y?
Theta and Si are to be thought of as variables; take x and y.
Theta and Si could equal anything from negative infinity to positive infinity, or go further, such as infinity plus infinity.
I hope this helps!
Theta and Si could equal anything from negative infinity to positive infinity, or go further, such as infinity plus infinity.
I hope this helps!
Whhat does he mean when he says, when we have two sides being equal (isosceles) then the base is equal? What is the side and what is the base?
I kinda don't get the point of this concept... can someone please some it up?
What does 'si' (that cactusshaped thing that Sal always uses) mean? It's the first time I've ever heard anyone use it in my whole life.
mdanivas, a.k.a. Pants
mdanivas, a.k.a. Pants
This is Theta: ϴ and this is psi: ψ and they just are GrΣΣk letters used to mean unknown in Geometry.
Psi is simply a Greek letter used to represent various things in mathematics, in this case it is used as a variable to represent the inscribed angle of a circle. http://en.wikipedia.org/wiki/Psi_(letter)
Oooohhhh.
mdanivas, a.k.a. Pants
mdanivas, a.k.a. Pants
I know that this is a kind of stupid question, but what's the inscribed angle of a circle?
mdanivas, a.k.a. Old Spice Man
mdanivas, a.k.a. Old Spice Man
how would any non physicist use this in their life?
A greek letter used to note the inscribed angle...and is it psi
at 2:01 what does si has mean?
Psi (not si) is a letter in Greek alphabet (Ψ). Mathematicians use Greek letters to write angles. They often use other letters : α(alpha), β(beta), γ(gamma), θ(theta)
How would you solve PSQ=3y15 and PRQ=2y +25?
The problem is: Find m<PSQ if M<PSQ=3y15 and m<PRQ= 2y+25
< = angle sign
< = angle sign
You would have to tell me how PSQ and PRQ are related. Which one is the inscribed angle and which one is the central angle?
A circle with an area of 49π square centimeters is inscribed (tightly inside of) a square. What is the area of the square?
could u tell me the proof of the inscirbed amgle theroem, case 2?
what is the angle called when it is neither central nor inscribed? and what is the formula for it. does the arc equal the angle or is it the angle half of the arc? help!
would the central angle also show the measure of the arc (number of degrees)?
Only thing to do in exercise: blue angle divided by 2 = orange angle and orange angle times 2 = blue angle. Do that for all the 3 exercise on this and you get 100% :) logic
what does si represent
its psi not si , and its a greek character. its just used to represent a random number , just like we use x , y etc.
Sal proved that theta is twice psi in the first case, but it seems (at least to me) that he used the fact that theta is "supposed" to be twice as much as psi to prove the other two cases instead of proving them all from scratch. Can anyone explain if I'm missed something?
Well, in 2nd case you can see that psi1 have same arc as teta1 and that exactly same as the first case
that's why Sal write that psi1 = 1/2 teta1
that's because we already learning that in 1st case!
that's why Sal write that psi1 = 1/2 teta1
that's because we already learning that in 1st case!
is the diameter the line that goes across the circle?
Yes, the diameter is the line across the entire circle and it can be confused with the radius which only goes halfway across the circle...both go throuch the exact center of the circle.
Psi is simply a greek letter that Sal has chosen to represent an angle. It is a variable, just like x, y, z or theta.
what value does SI have i can not find a video about it
So how do you work out trying to find inscribed angles with a quadrilaterals inside of circles? Do you just separate the angles?
how much rays are on this circle?
A state park decided to keep track of how many people use each of its two hiking trails each year.
Pescado Lake Trail
35%
Sandia Crest
65%
Hiking trail usage
What is the measure of the central angle in the "Pescado Lake Trail" section?
Pescado Lake Trail
35%
Sandia Crest
65%
Hiking trail usage
What is the measure of the central angle in the "Pescado Lake Trail" section?
I am completely lost.
at about 02:18, he talks about psi and theta ,is the,si half of data?
Theta and Psi are letters in the Greek alphabet. They are commonly used to represent angles, the same way letters like a, b, c, or x, y, or z are commonly used as variables to represent unknowns in algebraic expressions. He could have used any letter to represent the angles. Hope this helps. Good Luck.
LOL!
not data! its theta(θ)!
And the other one is psi, not si
not data! its theta(θ)!
And the other one is psi, not si
yes psi is half of theta
Why is it when psi and theta are on the diameter that theta is automatically 2 psi? Sal does this through out the video with psi 1 and 2 and theta 1 and 2. Is there a rule I don't know about?
Basically, in this entire video when he says theta and psi (not sure if thats how theyre spelled) do they have an absolute value or are they like variables??
These are greek letters and are used as variables.In greek Ψ (Psi) means PS and Θ (Theta) means TH.
These are greek letters (spelled theta and psi) and they are just used as variables.
Can someone please explain what sy and data is! HELP
its not data.
its theta(θ)
its theta(θ)
Psi (not si) is a letter in Greek alphabet (Ψ). Mathematicians use Greek letters to write angles. They often use other letters : α(alpha), β(beta), γ(gamma), θ(theta)
You know how Sal only drew triangles in the circle in the video? What if it was a quadrilateral n the circle instead?
instead of doing half the central angle for the inscribed angle couldn't you just half the arc angle because it is equal to the central angle subtending the arc
Why are greek and latin letters used so commonly in Chemistry Physics and Mathematics?
Mostly Greek letters are found in physics like for instance Δ (delta), although words like
scalars and vectors which are also used in physics come for latin words scalaris and vehere
scalars and vectors which are also used in physics come for latin words scalaris and vehere
I think almost every latin letter is also found in either the greek or english alphabet. However, I think greek letters are used mainly to avoid confusing. By adding the two alphabets together, you more or less doubles the number of symbols available. This is especially useful if you have multiple formulas with several variables. You could have used other symbols but mathematicians and scientists seem to stick to the conventions although they do not always admit it :)
Are si and thetha just terms used for angles or are inscribed and central angles just called 'si' and 'theta'?
correction: psi and theta
and yes, yes they are.
and yes, yes they are.
Can anyone explain this to me in real life applicable terms?
at 2:22, I saw a circle.
So what it is not a question
Sal said that 2 of the si or base angles equal to theta .but then on the video, he said that the complementary angle to the isosceles triangle is theta, not the vertical angle!! How is that so?( app. 5:00 minutes)
dont understand..
how do you spell it, data? sy?
how do you spell it, data? sy?
By subtended, do you mean intercepted (when referring to arcs)
Wouldn't Psi equal half of 0.10 to the power of two of Beta, or is Sal doing this way more systemically?
What does beta mean and that y thing mean
Sorry I have not been back on in forever. So what ur saying is that they ar like variables?
Think about it. There is a alpha and a beta, for example, alphabet. If you still don't get it, comment back.
Where did the 1/2 theta come from?
Does it have to be a circle?
can you at least give an example with numbers not much of variables but only if needed please
What is bata? Or is it data? What does it mean?:[
Theta is how it is spelled and can mean many things but for math, it means a plane angle. it is the 8th letter of the greek alphabet and means TH. The symbol looks like this Θ
a Chadic language spoken south of Lake Chad
what does he mean by "subtending" ?
In geometry, subtend means to extend under or be opposite to, as in a chord or an angle subtending an arc. Hope this helps. Good Luck.
making an angle between them.
I need help what does beta mean
what is si (sie)?
Psi (uppercase Ψ, lowercase ψ) is a greek letter and like other greek letters it is often used in mathematics and physics. In this video, it is used to denote the inscribed angle 0:19 (the one where the vertex sits on the circumference of the circle). But I think it is more commonly used to denote the wavefunction of a particle in quantum mechanics for instance in the schrödinger equation. That is if you can call quantum mechanics common ;)
Assuming you mean psi, ψ, it is a Greek letter that is commonly used as a variable for angles.
how do you use this in everyday life?
At 0:35, what does subtend mean? Also, why does Sal use Psi one and Psi two etc, instead of just using different letters?
I just had a silly question about when he said, the rays intersect the circle. can line segments also intersect? or would we rather define that as something else like touching or something? I hope that I was clear enough in asking my question!
Yes, the line segments can also intersect, the only difference is that the line segments have a finite length and the rays go on forever.
ever ever ever..ever......
I can't find a video for finding the length of the arc of a circle. I only found an exercise, and couldn't figure out how to complete the equation (when I tried to get hints for the problem, I couldn't follow all the steps they took). Anyone have any tips, or info on a video?
what does he mean by psi
no it's a greek character
no he means Psy from gangnam style
At 7:55, how do we know that psi 1 is congruent to psi 2?
I watched it a few times. It doesn't seem that Sal says they are congruent. What he does say is that psi 1 is 1/2 of theta 1 and psi 2 is 1/2 of theta 2, which is based on what he did earlier. He also says that psi 1 + psi 2 = psi, which is clear from the diagram.
can't be as the left chord moves closer to thr edge of the circle the angle becom es infitely small. while the inscreibed central remains the same. psi can't be i/2 theta???
if you move either of the chords the central angle must change it like opening those weird closet doors if you open one and move one of the halves the other half moves too
what is subtended?
is it always length * width ?
thx sooo much that helps alot !!!!!!!!!!!
For area of squares and rectangles, yes. For area of triangles you use 1/2bh. For the area of a circle you use pi(r)^2. It changes for every shape.
What is does it mean by 'Psi'?
Psi is a Greek letter that Sal is using as a variable to identify the inscribed angles.
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