# 3: Plane and Spherical Trigonometry

*Thumbnails: If \(C \) is acute, then \(A \) and \(B \) are also acute. Since \(A \le C \), imagine that \(A \) is in standard position in the \(xy\)-coordinate plane and that we rotate the terminal side of \(A \) counterclockwise to the terminal side of the larger angle \(C \). If we pick points \((x_{1},y_{1}) \) and \((x_{2},y_{2}) \) on the terminal sides of \(A \) and \(C \), respectively, so that their distance to the origin is the same number \(r \), then we see from the picture that \(y_{1} \le y_{2} \). Image constructed by *Michael Corral (Schoolcraft College).