QUESTION:
I'm having a hard time figuring this problem out. I've looked through my lectures and cannot find a problem that relates to this one. I do have my identities pulled up in front of me. I'm unsure where to start though. Can someone give me a kick in the right direction. Also could someone give me some rep points so I can format my questions nicer next time. Thanks
PROBLEM:
Find $\tan \theta$ if $\sin(\theta/2) = 3/5$
Best Answer
$$ \sin^2\frac\theta2+\cos^2\frac\theta2=1. $$ So $$ \left(\frac35\right)^2+\cos^2\frac\theta2=1. $$ Given that, you can find that $\cos\frac\theta2=\pm\text{something}$. Once you've got $\sin\frac\theta2$ and $\cos\frac\theta2$, use the fact that $\sin\theta=2\sin\frac\theta2\cos\frac\theta2$ and $\cos\theta=\cos^2\frac\theta2-\sin^2\frac\theta2$ (double-angle formulas).
Then there's still a "$\pm$" question.