Question

For what numbers $\theta$is$f\left(\theta \right)=\tan \left(\theta \right)$ not defined?

Short answer

When$\theta$is odd multiples of$\frac{\pi }{2}$

Step-by-step solution

Given information

We are given a tan function

Explanation

We have,

$$\begin{gathered} \tan \left(\theta \right) \\ =\frac{\sin \left(\theta \right)}{\cos \left(\theta \right)} \end{gathered}$$

Now the function will not exist when

$\cos \left(\theta \right)=0$

And$$\begin{gathered} \cos \left(\theta \right)=0 \\ When \\ \theta =\frac{(2n+1)\pi }{2} \end{gathered}$$