Alternatively, one could just use cos(x-90) in place of sine. Since it's arbitrary which we throw out, I say keep them both (also it allows you to intuitively associate sine and cosine with the legs of a right triangle in the unit circle)
I'd say sine and cosine get priority because they are much more well behaved and easier to work with than their reciprocals full of asymptotes and discontinuities
Alternatively, one could just use cos(x-90) in place of sine. Since it's arbitrary which we throw out, I say keep them both (also it allows you to intuitively associate sine and cosine with the legs of a right triangle in the unit circle)
I'm not sure why cos gets a pass but 'csc' doesn't. I'd absolutely argue the opposite in terms of intuitive associations.
I'd say sine and cosine get priority because they are much more well behaved and easier to work with than their reciprocals full of asymptotes and discontinuities