To take the shortest path to Calculus, we don't need to cover all the trigonometric identities. We just need to
- define the sin & cos function in terms of a right triangle
- teach the unit circle coordinate values of simple angles:
0, pi/6, pi/4, pi/3, pi/2, ...
Basic sin & cos can form the rotation matrix, which will later lead to hyperbolic rotations of Special Relativity.