1. The problem statement, all variables and given/known data I want to derive the trig identities starting with rotation on the plane. 2. Relevant equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ 3. The attempt at a solution What if I wanted to rotated through any angle $$ψ$$. Then $$ x'' = x'cosψ - y'sinψ $$ $$ = (xcosθ - ysinθ)cosψ - (xsinθ + ycosθ)sinψ $$ $$ = xcosθcosψ - ysinθcosψ - xsinθsinψ +ycosθsinψ $$ I'm concerned about having x's and y's still. Hint?