0
$\begingroup$

$$\tan(u) = 2, \ \ \ 0 < u < \frac{\pi}{2}\\ \tan(v) = 3, \ \ \ 0 < v < \frac{\pi}{2}$$

What is $u + v$?

I know that both angles are in the first quadrant in the unit circle. How do I calculate the sum of the angles? (Without calculator of course.) I'm not sure on how to think, or what methods to apply. I know that $\tan(u) = \frac{\sin(u)}{\cos(u)}$, but I'm not sure that helps here.

$\endgroup$
2
  • $\begingroup$ If you know what $\arctan$ is, the problem is almost solved, and the answer is $u+v=\arctan 2 + \arctan 3$. $\endgroup$
    – Lehs
    Nov 27 '14 at 10:14
  • $\begingroup$ @Lehs Won't I need a calculator for that? $\endgroup$
    – lawls
    Nov 27 '14 at 10:15
3
$\begingroup$

Use the formula $$\tan(x+y) = \frac{\tan x + \tan y}{1 - \tan x\tan y}.$$

$\endgroup$
0
$\begingroup$

$$\tan(u+v)=-1\implies u+v=n\pi-\frac\pi4$$ where $n$ is any integer

As $0<u+v<\pi, n=1$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.