Question

Explain why $y=\tan \left(\theta \right)$ has no amplitude.

Short answer

Because the maximum and minimum value of tangent function is undefined. Therefore, the given function$y=\tan \left(\theta \right)$ has no amplitude.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=\tan \left(\theta \right)$.

Step 2. Explanation.

Since the given function $y=\tan \left(\theta \right)$ has no maximum and minimum values because the maximum and minimum value of tangent function is undefined. Therefore, the given function $y=\tan \left(\theta \right)$ has no amplitude. It can also be interpreted from the graph of $y=\tan \left(\theta \right)$ shown below that the maximum and minimum values of $y=\tan \left(\theta \right)$ is not defined. So, the given function has no amplitude.

Step 3. Conclusion.

Because the maximum and minimum value of tangent function is undefined. Therefore, the given function $y=\tan \left(\theta \right)$ has no amplitude.