What are people doing (in particular in games) that makes the calls to sin and cos take a noticeable chunk of time?
Calculating object rotations/orientations.
Do people really do that? 3D rotations are easily encoded using unit-length quaternions, and 2D rotations using unit-length complex numbers. If you use those, you basically don't need any trigonometric functions for rotations/orientations, just multiply-adds. I thought that's what everyone would be doing.