# Find values of sin and cosine given terminal arm

Question: The terminal arm of angle A goes through a point P. In each of following cases, find the exact values of sin(A) and cos(A) in the simplest radical form:

1) P(0, 5)

2) P(-8, 15)

3) P(√3, -1)

4) P(-4, -4)

I understand how to find the sign and cosine for unit circles, but what do you do when it is not a unit circle?

## 2 Answers

Find exact values by plotting on a graph and use pythagorean theorem to find hypotenuse. For example in 2) hypotenuse is sqrt(64 + 225) and sinA is sin (y / hypotenuse) or sin (15/ 17). Then you can do the same for cos, x over the hypotenuse.

You have to scale the entire image down so $P$ is on the unit circle. Scaling doesn't change the angle

1) Make $P$ be on the unit circle by dilating by $5$. Now $P=(0,1)$, making $\sin a = 1$ and $\cos a = 0$

2) In this case, this is a simple 8-15-17 triangle. Dilate the triangle by 17 to get $\sin a = \frac{-8}{17}$ and $\cos a = \frac{15}{17}$

Now that you understand, try the rest by yourself!