Trigonometry question?

Question

Suppose P(-5/6,y) is a point on the unit circle in the third quadrant. let θ be the radian measure of the angle in standard position with P on the terminal side, so that θ is the circular coordinate of P. Evaluate all the circular functions of θ.

Answer 1

If (x,y) is a point on the unit circle, x²+y²=1.

 

In the third quadrant, x and y are both negative.

 

Since x = -5/6, we have (25/36) + y² = 1

 

                                                y² = 11/36

 

                                                y = -√(11)/6

 

cosθ = x = -5/6                secθ = 1/cosθ = 1/x = -6/5

 

sinθ = y = -√(11)/6           cscθ = 1/sinθ = 1/y = -6√11/11

 

tanθ = y/x = √(11)/5         cotθ = 1/tanθ = x/y = 5√11/11