Question

Which function is undefined when theta=pi/2 radians?

Answer 1

tan ∅ and cot ∅

tan ∅ is undefined for ∅ = $\frac{\pi }{2}$

and since cot ∅ = 1/ tan ∅ then cot ∅ is also undefined for ∅ = $\frac{\pi }{2}$

Answer 2

Answer:

$\tan\theta$ is undefined when $\theta=\frac{\pi}{2}$  radians.

Step-by-step explanation:

Given :  $\theta=\frac{\pi}{2}$  radians  .

To find : Which function is undefined  ?

Solution :

To check which functions are undefined  put the value of $\theta=\frac{\pi}{2}$,

1) $\cos\theta$

$\cos\theta=\cos\frac{\pi}{2}=0$

2) $\cot\theta$

$\cot\theta=cot\frac{\pi}{2}$

$\cot\theta=\frac{cos\frac{\pi}{2}}{sin\frac{\pi}{2}}$

$\cot\theta=\frac{0}{1}$

$\cot\theta=0$

3)  $\csc\theta$

$\csc\theta=cosec\frac{\pi}{2}$

$\csc\theta=\frac{1}{sin\frac{\pi}{2}}$

$\csc\theta=\frac{1}{1}$

$\csc\theta=1$

4)

$\tan\theta=\tan\frac{\pi}{2}$

$\tan\theta=\frac{sin\frac{\pi}{2}}{cos\frac{\pi}{2}}$

$\tan\theta=\frac{1}{0}$

$\tan\theta=\infity$

Therefore, $\tan\theta$ is undefined when $\theta=\frac{\pi}{2}$  radians.