How do you solve $1+sin(2\theta)=0.0368$

Question

$$ 1+sin(2\theta)=0.0368 $$

I'm studying for my physics final and I can not remember how to solve the above equation. I thought I could just move the 1 to the other side, and then take the inverse sine, and then divide by two, but I'm not getting the correct answer. I don't remember doing this in algebra but I'm sure we did at some point.

Thank you.

Answer 1

but I'm not getting the correct answer

Actually, you are. :-) The problem is that you assume that there is only one answer, when, in fact, due to the periodicity of trigonometric functions, there are an infinity of them. The whole idea is to select the one that matches the other conditions or restrictions imposed on it by the rest of the text. Use the fact that $~\sin x=\sin(\pi-x)=\sin(2\pi+x)$.