Tangent and cotangent/Monotonicity behavior/Fact
The
real tangent function induces a bijective, strictly increasing function
and the real cotangent function induces a bijective strictly decreasing function
real tangent function induces a bijective, strictly increasing function
![{\displaystyle ]-\pi /2,\pi /2[\longrightarrow \mathbb {R} ,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f54b80848470e2b293193379bd774648a7d69df6)
and the real cotangent function induces a bijective strictly decreasing function
![{\displaystyle [0,\pi ]\longrightarrow \mathbb {R} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/014d0207862d72a4533c62948f6bae80d18e9964)