You Do Need power plug adapter while traveling from Cook Islands to Burkina Faso.

Here is Why You Need An Adapter

The outlet and plug type used in Burkina Faso are C and E and in Cook Islands is I. This is how they look like.

Cook Islands

In Cook Islands, outlets of type I are in use.

Type I

Burkina Faso

In Burkina Faso, outlets of type C and E are in use.

Type C

Type E