Question

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

Answer 1

`2pi.`

Explanation:

Suppose that, `f(x)=e^cosx.`

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

That is to say, `cos(x+2pi)=cosx.`

Hence, `f(x)=e^cosx=e^{cos(x+2pi)}=f(x+2pi).`

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