As far as I understand, everything can be expressed using the four basic trigonometric functions (sine, cosine, tangent, cotangent), so why were the reciprocals of sine and cosine, the cosecant and secant functions, introduced?
Is it just a matter of simplification and compression in writing, or are there some historical reasons?
I appreciate your input!
P.S. I just can't use 'sec' and 'csc'. I always end up converting them to sine and cosine :P And my results are always expressed in sin and cos, is that wrong?