# How do you find the period of  e^cosx?

Jun 15, 2016

$2 \pi .$

#### Explanation:

Suppose that, $f \left(x\right) = {e}^{\cos} x .$

Now we know that the Principal Period of cosine fun. is $2 \pi .$

That is to say, $\cos \left(x + 2 \pi\right) = \cos x .$

Hence, $f \left(x\right) = {e}^{\cos} x = {e}^{\cos \left(x + 2 \pi\right)} = f \left(x + 2 \pi\right) .$

This shows that the reqd. period of $f$ is $2 \pi .$