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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 3

Lesson 6: The graphs of sine, cosine, and tangent

# Intersection points of y=sin(x) and y=cos(x)

Sal draws the graphs of the sine and the cosine functions and analyzes their intersection points. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Im a little confused as how Sal knew that the inbetween point between π and 3π/2 was 5π/4? •   Take the average: (π + 3π/2)/2
= (2π/2 + 3π/2)/2
= (5π/2)/2
= 5π/4
• Why does trigonometry use Greek letters (like alpha, beta, theta) rather then the common variable names (like x, y, n, or z)? •   Many parts of Mathematics use different letters. For instance, algebra uses mostly x, y, z and sometimes w. However, in number theory, mostly n and m are used. In vectors, the usage of i, j, k is very common, and when defining lines, I remember usually using r and s. When expressing prime numbers, it's almost always p and q, and with functions, f, g and h. When speaking about points, it's always A, B and C, sometimes D, E, F, G, M, N many times P, Q, R, S, T, for centers it is O, G, H, I, and some even usually add X and Y.

For parameters, it is not unusual using lambda and mu, and for derivatives it is delta. And I guess that for angles, we usually use alpha, beta, and gamma, although some use instead theta and phi.

I don't think there is much meaning for the usage of letters in distinct areas, but it is sometime easy to remember them that way, as they are usually used in similar fashion. For example, when you see point O, it is probably the center of a circle, when you see n and m, it is probably either a series or a number theory problem, if it's x, y and z it is either algebra or analytic geometry, and when you see alpha, beta and theta you can easily suppose that it s an angle problem.
• I'm curious as to whether there is some relationship of quadratics going on here with sine and cosine functions. When I look at the graphed functions, they resemble symmetrical parabolas that you would typically find with a quadratic function that just loop and keep going. Does anyone know if this is a coincidence or is there actually some relationship with trig functions like sine and cosine and the squares of some numbers? •  That's an interesting observation. Unfortunately, in nature there are a lot of things that look a little like parabolas that actually aren't, and the sine wave is one. Strangely enough, another one that isn't is if you hang a chain between two points it looks like it hangs like a parabola, but it's actually a different curve called a catenary.
• I don't really understand what Sal did at with the root of two. He said 'we can rationalise the denominator here', could anybody explain what he does? • Rationalising the denominator means removing the radical sign. The radical sign is that which is used to denote square root. We multiply both the numerator and the denominator by a number such that the denominator has no radical sign. Multiplying both the numerator and the denominator by the same number doesn't change the value of the number. For example, 2/3 = 4/6. So here, if we multiply both the numerator and the denominator by sqrt2, the denominator becomes 2 and the radical sign is removed.
At , you can see that 1/sqrt2 has been converted into sqrt2/2
Just for your information, sqrt2/2 = 0.7071 and you get the same answer when you divide one by sqrt2. This kind of verifies that we have not changed the value of the expression by rationalising the denominator.
• is it necessary to remove a radical sign from denominator • I am really puzzeled about the - portion of the video where Sal goes from a^2 =1/2 to
a = 1/sqrt 2....how did he do that? • You have 2a^2 = 1
(divide each side by 2) a^2 = 1/2
(take square root of each side) sqrt(a^2) = sqrt (1/2)
(left side) sqrt(a^2) = 1
(right side) sqrt(1/2) = sqrt(1)/sqrt(2); sqrt(1) = 1, sqrt(2) = sqrt(2) so sqrt(1)/sqrt(2) = 1/sqrt(2)
giving us..............a = 1/sqrt(2)
Then you multiply each side by sqrt(2)/sqrt(2) (which is 1)
a * sqrt(2)/sqrt(2) = a
1/sqrt(2) * sqrt(2)/sqrt(2) = (1*sqrt(2))/(sqrt(2) * sqrt(2)) = sqrt(2)/2
thus
a = sqrt(2)/2
• Where is 'tan' in all of this? I haven't seen it once yet in this section, why is that? I sort of get that the X axis represents 'cos' and the Y axis represents 'sin', but what about tan? Thank you. • I don't really understand why Sal, in these videos, uses pi and radians instead of 90, 180, 270, etc. degrees. Is there a difference between the two and is on better than the other for this topic? • At isnt he marking wrong? He is marking cosine on the Y axis, but on the begining of the video he said cosine of data is the X, axis! And sine was the Y axis! Now im really confused! • I understand the confusion. When he said cosine of theta is the x-axis, he was basically saying "Instead of the x-axis and integers (i.e. -2, -1, 0, 1, 2 ect...) we are going to call it the theta-axis and use radians." Also, instead of saying cos(theta) = y-axis he mixed up the measurement for the two axis. One axis has been turned into radians (theta, cis(theta)), the other has been left in integer number form. (x/y form). 