Question

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

Answer 1

Answer:

Option 4  $tan\theta$ is undefined.

Step-by-step explanation:

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

To find : Which function is undefined

Solution : Put  $\theta=\frac{\pi}{2}$ in all the given options to check which are undefined

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

$Cot\theta=cot\frac{\pi}{2}=\frac{cos\frac{\pi}{2}}{sin\frac{\pi}{2}}=\frac{0}{1}=0$

$Csc\theta=cosec\frac{\pi}{2}=\frac{1}{sin\frac{\pi}{2}}=\frac{1}{1}=1$

$tan\theta=tan\frac{\pi}{2}=\frac{sin\frac{\pi}{2}}{cos\frac{\pi}{2}}=\frac{1}{0}=infinity$

Therefore, we get that$tan\theta$ is not defined or undefined.

Answer 2

We know that tanθ = sinθ/cosθ

For a number to be undefined, the denominator must equal to 0. At π/2, the cosθ value is 0 and sinθ is 1. Hence, tan(π/2) is undefined. 

Hope I helped :)