This function's Taylor series begins x plus one-th
This function's Taylor series begins x plus one-third x cubed plus two-fifteenths x to the fifth, and its derivative is secant squared. Its Pythagorean identity says that it squared plus one equals the secant squared. Like its reciprocal, this function has period (*) pi and equals 1 for an input of 45 degrees. For 10 points, name this trig function equal to sine over cosine, or in a right triangle, the opposite side over the adjacent side.
This function's Taylor series begins x plus one-third x cubed plus two-fifteenths x to the fifth, and its derivative is secant squared.