Respuesta :

check the picture below, notice the red asymptotic lines.

now, recall that 

[tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ tan\left( \frac{\pi }{2} \right)=\cfrac{sin\left( \frac{\pi }{2} \right)}{cos\left( \frac{\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{1}{0}} \\\\\\ tan\left( \frac{3\pi }{2} \right)=\cfrac{sin\left( \frac{3\pi }{2} \right)}{cos\left( \frac{3\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{-1}{0}}[/tex]
Ver imagen jdoe0001

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