Question

Given the trigonometric equation:

Answer 1

Make use of your knowledge of the values of the sine function to determine angles where sin(y) = -(√3)/2. Then translate those angles to different quadrants or add different multiples of 360° (or 2π radians) as needed to find as many solutions as you want.

sin(y) = (√3)/2 for y = 60° (or π/3 radians)

The sine will be negative for angles in the 3rd and 4th quadrants whose reference angle is 60°. Those angles are 180°+60° = 240°, and 360°-60° = 300°. These are two of your solutions. You can add 360° to either of them to find another solution: 240°+360° = 600°, for example.

The solution set includes y = ...

... 240°, 300°, 600°

or

... 4π/3, 5π/3, 10π/3 radians