How do I deal with sines or cosines greater than $1$? When I'm solving trigonometric equations, I occasionally end up with a sine or cosine that's greater than $1$ -- and not on the unit circle. For example, today I had one that was $3 \tan 3x = \sqrt{3}$, which simplified to $\tan 3x = \frac{\sqrt{3}}{3}$, which simplified to $\sin 3x = \sqrt{3}$ and $\cos 3x = 3$. So far as I know, I can't divide this by $3$ (to isolate $x$) until I get angles with a sine of $\sqrt{3}$ and a cosine of $3$, respectively. So, how do I reduce this cosine so that I can find an angle on the unit circle with that cosine? Or, am I doing something very wrong to get this as a cosine in the first place? 
Thanks!
evamvid

Hint: If you are solving $\tan x = a/b$, you have to realize $a/b$ can be written as $(a/c)/(b/c)$ for any nonzero $c$. You have to pick a value of $c$ before you can try to do that. Look at $c= \pm \sqrt{a^2+b^2}$ and see if either of those values gets you further.
