Circles
Inscribed angles
None
Inscribed angle theorem proof
Proving that an inscribed angle is half of a central angle that subtends the same arc.
Discussion and questions for this video
 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 whose vertex sits on the circumference
 of the circle.
 So that is our inscribed angle.
 I'll denote it by psi  I'll use the psi for inscribed angle
 and angles in this video.
 That psi, 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 psi.
 It is an inscribed angle.
 It sits, its vertex sits on the circumference.
 And if you draw out the two 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 psi.
 It's all very fancy words, but I think the idea is
 pretty straightforward.
 This right here is the arc subtended by psi, where psi 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 psi, this angle right here is theta.
 What I'm going to prove in this video is that psi is always
 going to be equal to 1/2 of theta.
 So if I were to tell you that psi 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 psi 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 an inscribed angle, but one of the chords
 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 psi.
 If that's psi, 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 psi.
 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 psi, then you would also
 know that this angle is also going to be psi.
 Base angles are equivalent on an isosceles triangle.
 So this is psi, that is also psi.
 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 they kind of form a 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 psi  this psi plus that psi plus psi 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.
 psi plus psi is 2 psi minus theta is equal to 0.
 Add theta to both sides.
 You get 2 psi is equal to theta.
 Multiply both sides by 1/2 or divide both sides by 2.
 You get psi 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 of 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 psi is or whatever theta is, psi's going to be 1/2
 of that, or whatever psi 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
 chords 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 chords 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 psi 1, that angle as psi 2.
 Clearly psi 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 psi 1 is going to be
 equal to 1/2 theta 1.
 And we know that psi 2 is going to be 1/2 theta 2.
 Psi 2 is going to be 1/2 theta 2.
 So psi, which is psi 1 plus psi 2, so psi 1 plus psi 2 is going to
 be equal to these two things.
 1/2 theta 1 plus 1/2 theta 2.
 psi 1 plus psi 2, this is equal to the first inscribed
 angle that we want to deal with, just regular psi.
 That's psi.
 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 psi 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 chords.
 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 chords that defines the
 angle, just like that.
 And let's say that is the other chord 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 psi 1.
 How do we find the relationship between psi 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 psi 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 psi
 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 chords that forms the angle.
 So psi 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 chords 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.
 Psi 1 plus psi 2.
 Right, that larger angle is psi 1 plus psi 2.
 Once again, this subtends this entire arc right here, and it
 has a diameter as one of the chords 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 psi 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.
Before asking, please make sure you've checked the top questions below and our FAQ. Thanks!
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!
They are Greek letters usually used to denote angles. Variables are a bit different as they denote quantities.
theta is used to represent angles often, and i dont know about psi
just a varuble like x
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.
what is sy and data?
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.
oh thank you!
well at 0:21 it is showing a y with a middle spear this is also called PSI this is a greek math symbol commonly used in physics to represent wave functions in quantum mechanics. here is a link to a chart of many different symbols used by the greek.
http://www.sunilpatel.co.uk/wpcontent/uploads/2010/08/LowercaseGreekSymbols.jpg
http://www.sunilpatel.co.uk/wpcontent/uploads/2010/08/LowercaseGreekSymbols.jpg
its psi and theta and they are greek letters
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
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.
Greek letters
not DATA, THETA (at first I thought it was Beta). Psi and Theta are Greek letters (ψ and ϴ).
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.
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.
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.
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...
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.
Psi is a Greek letter. In this case, it's being used to denote a variable (like x or y in algebra). Evidently the subtitle program doesn't recognize silent P's.
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)
I never seen Psi used as a variable like that. Is there a convention to use it for inscribed angles?
Psi reminds me of the mind. It brings up words like psychic and psychology. I think Cupid had a girlfriend, name Psyche. Her name meant soul.
Psi reminds me of the mind. It brings up words like psychic and psychology. I think Cupid had a girlfriend, name Psyche. Her name meant soul.
The letter _psi_ (uppercase Ψ, lowercase ψ) is commonly used in physics, to present an understanding of functions in quantum mechanics. You are correct to state that it is used in words like Psychology. Although, I'm uncertain of the usage in Cupid's *wife* (not girlfriend). It could be that it refers to the mind( and soul, as you state).
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.
what are planes
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?
What would happen if the vertex of the inscribed angle is in between its endpoints?
why psi and theta instead of a or b? Do they stand for something or are they just variables?
a and b and other alphabetical variables are traditionally used in algebra.
For geometry, Greek alphabets like psi and theta are used. They are just variables like a and b.
For geometry, Greek alphabets like psi and theta are used. They are just variables like a and b.
What does Sal mean by the term, "subtended"?
```
Subtend
/səbˈtend/
• (of a line, arc, or figure) form (an angle) at a particular point when straight lines from its extremities are joined at that point.```
Subtend
/səbˈtend/
• (of a line, arc, or figure) form (an angle) at a particular point when straight lines from its extremities are joined at that point.```
so psi and theta are just variables like x and y?
then why is it used over x and y in trigonometry/geometry if they are essentially the same?
then why is it used over x and y in trigonometry/geometry if they are essentially the same?
psi and theta are used to represent angles. x and y are used in geometry to represent length of sides. That way if you see psi or theta you know they are talking about the angle.
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 :)
is vector geometry?
I don't think so. https://goo.gl/3P5XdQ
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.
Should we always use Si and Theta (< don't know if i spelled it right) or are they merely just being used as variables?
They are simply just used as variables. You can really use any shape or letter you would like. Even smiley faces could work in place. :)
Theta is usually used for an unknown angle. I am not sure about Psi.
When my teacher does these in class, she measures the outsides of an arc in degrees. Aren't we supposed to use regular measurements(Metric/Customary)?
You can use measurements like that if you are provided units in the first place. Usually you should use the units provided in the problem. If there aren't any units use radians or degrees. Arc length is usually always measured in radians which are convertible to degrees. Hope that helps!
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.
They say triangles are the strongest shape, but wouldn't circles be because they have no weak points to break under? Then we could have bridges and towers with circular supports like those ancient arches.
Well, this seems like more of a fantasy. Don't argue with Euclid or any geometry expert who knows more than you about geometry who says that triangles are the strongest shapes. Circles are not the strongest.
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.
Could you have used the Exterior Angle Theorem, where it says that an exterior angle of a triangle is equal to the sum of its two remote interior angles, in the first example and skipped the supplementary step?
Yep. I'm assuming he's keeping things basic to help keep the topic understandable, not using too much big terminology at once, I'd assume.
What is "theda"?
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
its psi; theta
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?
Could someone tell me what subtend means? Thanks.
Subtend means "intersect" or "encompass." For example, at about 2:00, the purple arc is subtended by psi and theta, that is, it is "inside" the angle.
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 do you find out Si and Theta?
I'm kind of confused. Can someone please explain this to me in a simpler way?
At 12:37, isn't the Theta 1 and Theta 2 a 90 degree angle? Cause Salman have drawn the angle as similar as 90 degree.
no,you can't say that thetas is 90 degrees just by observing and not measuring them
At 3:34, the Isosceles triangle that it says isn't really true, because the center isn't accurate enough.
If you measured it out, including the exact placement of the center along the diameter, then yes, you would probably find that the center is off by a little. However, because a diagram is a *representation* of something, some liberties can, and are, often taken with it. For instance, if you opened your math book and found a diagram of the base of the Statue Of Liberty along with it's measurements, you (probably) wouldn't think "Oh, well these are wrong. It says here that the height of the base is 89 feet, but on this diagram, it looks like it's only 2 inches.". That's because you know it's a diagram, and it's only showing you a general idea of what it might look like. Some diagrams are often equipped with a note, saying "diagram not drawn to scale", and that is the case with both the diagram of the Statue Of Liberty's Pedestal, and the diagram of the inscribed Isosceles triangle.
how would any non physicist use this in their life?
About 7:00, he said that the notation won't apply to all inscribed angles. Is there a special case where the notation doesn't apply?
Thank you Sal. You are an excellent math instructor and this site is beyond helpful.
However, you tend to use a lot of algebra. I find it would be more helpful to use simple arithmetic.
However, you tend to use a lot of algebra. I find it would be more helpful to use simple arithmetic.
at 8.10 Dont really understand how you can assume psi1 is equal to theta1. Isnt this a circular argument where you are assuming the conclusion for this particular repetition of the proof?
What is Si/Psi?
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?
When the angles form a triangle or a quadrilateral, how would you find the missing angles of the polygon inscribed in the circle?
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