Q.97 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given information

We are given a tan function

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