>As an API it might not be convenient but consider converting angles internally into a tuple of sin and cosine

My friend,

it's called a complex number. A unit complex number, to be specific.

>Recall rotation is a linear transformation with a matrix whose entries are in terms of sin and cosine.

That's what multiplication of complex numbers is.

Can't wait till people here rediscover that a 3D rotation matrix has an axis-angle representation whose composition is given by quaternion multiplication.

At that, children, is why learning mathematics is important.