1. The problem statement, all variables and given/known data A rotation ρ about the origin in ℝ2 drives the point P = (4,3) to the point ρ(P) = (3,4). Find the angle of rotation as well as its matrix notation. 2. Relevant equations Ok so I made a sketch and I realised I needed to find θ = θ1 - θ2 where θ1 and θ2 equal arctan(4/3) and arctan(3/4) respectively. I guess it's correct but then how would I work out the sin and cos of that angle θ without a calculator? SO. I worked out the cosine angle between the vectors 0P and 0ρ(P) and got cosθ = 24/2√25 But now I don't know how to work out the sine! My goal is to replace everything into the ℝ2 rotation matrix (row 1; row 2): (cosα -sinα; sinα cosα) and express as g(x) = Ax + v Thanks a lot!