`sin(theta) = -1/2` Find two solutions of each equation. Give your answers in degrees (0 <= theta <= 360) and radians (0 <= theta <= 2pi)

nisarg | Student

Sine and cosine at max are 1.  Cosine is X and Sine is Y. The values of them repeat as their graphs are waves. As you can see here 

 So here `7pi/6`  and `11pi/6`   can both equal theta

theta can be 210 degrees or it can be 330 degrees

kspcr111 | Student

As wiggin42 stated is right 

`sin(theta) ` is negative so `theta` lies between `pi` to `2pi` or `180^@` to `360^@`

and

`sin(theta) = -1/2`

=> `theta = sin^-1(-1/2)`

`theta = 210 ^@ or 330^@ ` in degrees

and 

`theta = 7pi/6 or 11pi/6` in radians

the answer in radians was not given by wiggin42 .....so i gave the answer

Wiggin42 | Student

`sin(theta)` is negative in the 3rd and 4th quadrants. Looking at a unit circle, `sin(theta) = -1/2` when `theta` equals 210 and 330 degrees.