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The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to co-.
The function is the multiplicative inverse to the sine, and is called the cosecant.
Later aerial reflectors were actually shaped with a cosecant-squared curvature.
If is an integer multiple of, then the cotangent and cosecant functions above diverge.
The two expressions are derived from identities involving the cotangent and cosecant functions.