Prove that the real sine function induces a bijective, strictly increasing function
and that the real cosine function induces a bijective, strictly decreasing function
![{\displaystyle [-\pi /2,\pi /2]\longrightarrow [-1,1],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/527f8bc31212ec82e3778cde36b1ed32192bf657)
![{\displaystyle [0,\pi ]\longrightarrow [-1,1].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8dbd9728b307c63938254cd4e4aff49bc8e2f2a7)