Insulation, Radiant and Vapor Barriers - Insulating under eaves

I am not sure what to call the area that I want to insulate. I bought an old house recently and there is a space under the eaves that is accessible from the bathroom. The area is roughly in the shape of a right triangle with the roof forming the slope. This space forms part of my bedroom wall and most of one bathroom wall. The bathroom is cold in winter and hot in the summer. There is currently no insulation in this space. The previous owners tacked up some cardboard. I have some questions about how to best insulate this space.

1. I am assuming that it would be best to remove the cardboard, correct?

2. Do I insulate the floor, walls, and roof?

3. Do I need some type of vapor barrier?

Any help would be appreciated. Thanks.

You should insulate the wall or ceiling that meets the heated space. If these walls are outside walls they should be insulated using a vapor barrier. If their are vents in your eaves you do not want to cover these areas with insulation.

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Thanks for your help.