You Do Need power plug adapter while traveling from Costa Rica to Cocos (Keeling) Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) Islands is I and in Costa Rica are A and B. This is how they look like.

Costa Rica

In Costa Rica, outlets of type A and B are in use.

Type A

Type B

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I