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Find the value of $\tan(\large\frac{-25\pi}{3})$

$\begin{array}{1 1}(A)\;-\sqrt 3&(B)\;\sqrt 5\\(C)\;\sqrt 7&(D)\;\sqrt 6\end{array} $

1 Answer

Toolbox:
  • $\tan (\theta+n\pi)=\tan \theta$
$\tan(\large\frac{-25\pi}{3})$
$\tan (-\theta)=-\tan \theta$
$\Rightarrow -\tan(\large\frac{25\pi}{3})$
$\Rightarrow -\tan(8\pi+\large\frac{\pi}{3})$
$\tan (\theta+n\pi)=\tan \theta$
$\Rightarrow -\tan(8\pi+\large\frac{\pi}{3})$$=-\tan \large\frac{\pi}{3}$
$\Rightarrow -\sqrt 3$
Hence (A) is the correct answer.
answered Apr 22, 2014 by sreemathi.v
 
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