Question

Evaluate: $\tan \frac{\mathrm{\pi }}{2}$

Answer 1

To evaluate $\tan \frac{\mathrm{\pi }}{2}$

We know that the radian value of $\mathrm{\pi }={180}^0$

So, $\frac{\mathrm{\pi }}{2}=\frac{{180}^0}{2}$$={90}^0$

⇒ $\tan \frac{\mathrm{\pi }}{2}$$=\tan {90}^0$

We know the identity $\mathrm{tanA}=\frac{\mathrm{sinA}}{\mathrm{cosA}}$, we get

So, $\tan 90°$$=$$\frac{\sin {90}^0}{\cos {90}^0}$

$=$$\frac{1}{0}$ (From trigonometric table $\sin {90}^0=1$and $\cos {90}^0=0$)

$\frac{1}{0}$ is an undefined term due to its divisibility with zero.

Thus, $\tan 90°$is undefined