![{\displaystyle {\frac {2}{\pi }}x\leq \sin(x)\leq x{\text{ for }}x\in \left[0,{\frac {\pi }{2}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4a680ed652430cc1e24a8eea0259474d37b2551)
In mathematics, Jordan's inequality, named after Camille Jordan, states that[1]
![{\displaystyle {\frac {2}{\pi }}x\leq \sin(x)\leq x{\text{ for }}x\in \left[0,{\frac {\pi }{2}}\right].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6ca4fe8bbd3be495233e733ada39367cc378440)
It can be proven through the geometry of circles (see drawing).[2]
- ^ Weisstein, Eric W. "Jordan's inequality". MathWorld.
- ^ Feng Yuefeng, Proof without words: Jordan`s inequality, Mathematics Magazine, volume 69, no. 2, 1996, p. 126