Answer
tangent
Work Step by Step
Note that among the six trigonometric functions, sine and cosine and their respective reciprocal functions, cosecant and secant, have a period of $2\pi$.
Only tangent and cotangent have a period of $\pi$.
Note that the cotangent function is undefined for integral multiples of $\pi$, including $0$.
Thus, the function that satisfies all the given description is tangent.
