Question

The point (8, –15) is on the terminal side of an angle θ. What is sin θ ?

Answer 1

Let's calculate the hypotenuse of this right triangle:

(Hypotenuse)² = 8² + 15² = 289, Hypotenuse = √289 = 17.

a) If Ф is facing the largest side (15), then sinФ = opposite side / hypotenuse
and sinФ = 15/17 = 0.8823

b) If Ф is facing the smallest  side (8), then sinФ = opposite side / hypotenuse
and sinФ = 8/17 = 0.4705