Asked by Mary

Fine the complete exact value of sin x = -sqrt3/2.

I'm very lost as to how to even begin this problem.
Answered by Mary
Do I have to solve the right side of the equation first or bring it over to the left side?
Answered by Steve
If you're looking for a value for x, then you want to find all angles x where

sin x = -√3/2

Now, you should know that sin 60° = √3/2

sin x is negative in QII and QIII, so all solutions 0 <= x < 360 are x=180±60°. That would be 120° and 240°.

Now, sin x is periodic with period 360°, so you can add any multiple of 360° to those angles and the value of sin x is still -√3/2.

So, the complete solution is

x = 180±60° + 360n°, where n is any integer.

Answered by Steve
Oops. My bad. sin x is negative in QIII and QIV, so

x = 240° or 300°

add any multiple of 360° to those values.
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