SOLUTION: Find the values of the six trig functions for each angle θ in standard position if a point with the given coordinates lies on its terminal side. I do not know how to do pro

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Question 1004716: Find the values of the six trig functions for each angle θ in standard position if a point with the given coordinates lies on its terminal side.
I do not know how to do problems like these. My teacher assigned the worksheet without explanation. I don't expect you to solve all of the problems, but here they are. Please explain how to do problems like these! Thanks!
1. (3, 3)
2. (8, -2)
3. (4, 5)
4. (-4, 4)
5. (-5, 12)
6. (-2, 0)
7. (-5, -9)
8. (5, 0)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let theta be an angle in standard position and suppose that ( x , y+) is any point other than ( 0 , 0 ) on the terminal side of theta.
If r=+sqrt%28x%5E2%2By%5E2%29 is the distance between ( x , y+) and ( 0 , 0 ), then the six trigonometric functions of theta are defined by:

sin%28theta%29=y%2Fr
cos%28theta%29=x%2Fr
tan%28theta%29=y%2Fx
csc%28theta%29=r%2Fy
sec%28theta%29=r%2Fx
cot%28theta%29=x%2Fy

if theta contains the point
1. (3, 3)
=>x=+3 and y=+3, then
r=+sqrt%28x%5E2%2By%5E2%29
r=+sqrt%283%5E2%2B3%5E2%29
r=+sqrt%282%2A3%5E2%29
r=+3sqrt%282%29

sin%28theta%29=y%2Fr=3%2F3sqrt%282%29=1%2Fsqrt%282%29
cos%28theta%29=x%2Fr=3%2F3sqrt%282%29=1%2Fsqrt%282%29
tan%28theta%29=y%2Fx=3%2F3=1
csc%28theta%29=r%2Fy=3sqrt%282%29%2F3=sqrt%282%29
sec%28theta%29=r%2Fx=3sqrt%282%29%2F3=sqrt%282%29
cot%28theta%29=x%2Fy=3%2F3=1

I hope this will be enough to see how to do it. I am pretty sure you would be able to do the rest by your self.