Trigonometric functions/R/Inverse functions/Analytic properties/Section
Corollary
The real sine function induces a bijective, strictly increasing function
and the real cosine function induces a bijective, strictly decreasing function
Proof
See exercise.
Corollary
The real tangent function induces a bijective, strictly increasing function
and the real cotangent function induces a bijective strictly decreasing function
Proof
See exercise.
Due to the bijectivity of sine, cosine, tangent and cotangent on suitable interval, there exist the following inverse functions.
Definition
The inverse function of the real sine function is
Definition
The inverse function of the real cosine function is
Definition
The inverse function of the real tangent function is
Definition
The inverse function of the real cotangent function is