# How do you find lim tantheta as theta->(pi/2)^+?

Jun 8, 2017

$\tan \theta = \sin \frac{\theta}{\cos} \theta$

As $\theta \rightarrow {\left(\frac{\pi}{2}\right)}^{+}$,

$\sin \theta \rightarrow 1$ and

$\cos \theta \rightarrow {0}^{-}$. ($\cos \theta$ is negative in the second quadrant.)

Therefore, $\theta \rightarrow {\left(\frac{\pi}{2}\right)}^{+}$,

$\tan \theta \rightarrow - \infty$