Suppose there is a coordinate (-1, √3) at the end of a terminal arm and 𝜃 represents the angle in standard position. Determine the exact values of sin 𝜃, cos 𝜃, and tan 𝜃.

Question

I am stuck on this question, i am not sure how to do this, any help would be greatly appreciated!

Answer 1

Draw a right triangle

x=-1 and y=sqroot 3

solve for the hypotenuse by Pythagorean theorom h=2

x is adjacent y is opposite

sin= opp/hyp= Sqroot3/2

cos=adj/hyp=-1/2

tan = opp/adj= sqroot3

Answer 2

Cavan, here's how I would answer this:

If you draw the coordinate plane, it's easy to see that (-1, √3) lies in Q2

Drop a perpendicular from the point (-1, √3) to the X-axis. Now we have a right triangle with sides -1 and √3

By Pythagoras (-1)² + (√3)² = h² where h = hypotenuse

1 + 3 = h²

=> h = 2

Let's denote the angle by φ

sin φ = √3/2 sin is +ve in Q2

cos φ = -1/2 cos is -ve in Q2

tan φ = - √3 tan is -ve in Q2