Question

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

Cos theta
Cot theta
Csc theta
Tan theta

Answer 1

tan ∅ and cot ∅

tan ∅ is undefined for ∅ =
`(\pi )/(2)`

and since cot ∅ = 1/ tan ∅ then cot ∅ is also undefined for ∅ =
`(\pi )/(2)`

Answer 2

`\tan\theta` is undefined when
`\theta=(\pi)/(2)` radians.

Explanation:

Given :
`\theta=(\pi)/(2)` radians .

To find : Which function is undefined ?

Solution :

To check which functions are undefined put the value of
`\theta=(\pi)/(2)`,

1)
`\cos\theta`

`\cos\theta=\cos(\pi)/(2)=0`

2)
`\cot\theta`

`\cot\theta=cot(\pi)/(2)`

`\cot\theta=(cos(\pi)/(2))/(sin(\pi)/(2))`

`\cot\theta=(0)/(1)`

`\cot\theta=0`

3)
`\csc\theta`

`\csc\theta=cosec(\pi)/(2)`

`\csc\theta=(1)/(sin(\pi)/(2))`

`\csc\theta=(1)/(1)`

`\csc\theta=1`

4)

`\tan\theta=\tan(\pi)/(2)`

`\tan\theta=(sin(\pi)/(2))/(cos(\pi)/(2))`

`\tan\theta=(1)/(0)`

`\tan\theta=\infity`

Therefore,
`\tan\theta` is undefined when
`\theta=(\pi)/(2)` radians.