Question 135913
Find all exact solutions of the equation:
 
2sinx + 1 = 0

A trig equation will have exactly ONE ANSWER for each inverse function you use to solve it; an answer in exact form provides only those restricted range angles, nothing more.

Back to your question.

Treat this like a regular linear equation.  Do not allow the sine function to confuse you.

Subtract 1 from both sides.

Doing so, we get this:

2sinx = -1

Divide both sides by 2.

sinx = -(1/2)

In the unit circle, we are given two answers for sinx = -(1/2).

x = 210 degrees AND 330 degrees

Is this clear?

NOTE: Trig will be much more pleasant if you take time out to memorize the unit circle degree and radian measures.