Question

Which function is undefined when Theta = StartFraction pi Over 2 EndFraction radians?

cos Theta
cot Theta
csc Theta
tan Theta

Answer 1

Option 4
`tan`θ is undefined.

Explanation:

Given : θ
`\\=(\pi )/(2)` radians

To find : Which function is undefined

Solution : Put θ
`\\=(\pi )/(2)` in all the given options to check which are undefined

`Cos`θ
`=cos(\pi )/(2) =0`

`Cot`θ
`=cot(\pi )/(2)=(cos(\pi )/(2) )/(sin(\pi )/(2) ) =(0)/(1) =0`

`Csc`θ
`=cosec(\pi )/(2) =(1)/(sin(\pi )/(2) ) =(1)/(1)=1`

`tan`θ
`=tan(\pi )/(2) =(sin(\pi )/(2) )/(cos(\pi )/(2) ) =(1)/(0) =infinity`

Therefore, we get that
`tan`θ is not defined or undefined.