[Math] Projection of a Number onto a given Number Range.

I'm in a somewhat awkward situation - I guess the solution is fairly simple, yet I can't get it to work. I need to project a float number from one range (0 to 360) onto another float range ( 1 to -1). So that 0 is represented as 1, and 360 is represented as -1. (translating angle to Dot Vector).

For example: I want to project number 45.0 from the first Range (0 to 360) onto the second range ( 1 to -1) to find out it's equivalent in the second range.

How would this calculation look?