Question

Why is $\tan 90°$ undefined?

Answer 1

Trigonometric function:

From the property of tangent, we know that

$\tan \theta =\frac{\sin \theta }{\cos \theta }$ ………………….(1)

Substitute $\theta =90°$ in equation (1), we get

$\tan 90°=\frac{\sin 90°}{\cos 90°}$ ……………(2)

We know the value of $\sin 90°=1$ and $\cos 90°=0$

Substitute it in equation (2), we get

$\tan 90°=\frac{1}{0}$

We know that $\frac{1}{0}$ is undefined.

Hence, $\tan 90°$ is undefined.