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Do intervalo dado,
![\left[\pi,\frac{3\pi}{2}\right]=\\\\\pi\leq\,x\leq\frac{3\pi}{2}=\\\\\cos\pi\leq\cos\,x\leq\cos(\frac{3\pi}{2})=\\\\-1\leq\frac{2m}{5}\leq0=\\\\-1\cdot\frac{5}{2}\leq\frac{2m}{5}\cdot\frac{5}{2}\leq0\cdot\frac{5}{2}=\\\\\boxed{-\frac{5}{2}\leq\,m\leq0}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cpi%2C%5Cfrac%7B3%5Cpi%7D%7B2%7D%5Cright%5D%3D%5C%5C%5C%5C%5Cpi%5Cleq%5C%2Cx%5Cleq%5Cfrac%7B3%5Cpi%7D%7B2%7D%3D%5C%5C%5C%5C%5Ccos%5Cpi%5Cleq%5Ccos%5C%2Cx%5Cleq%5Ccos%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%29%3D%5C%5C%5C%5C-1%5Cleq%5Cfrac%7B2m%7D%7B5%7D%5Cleq0%3D%5C%5C%5C%5C-1%5Ccdot%5Cfrac%7B5%7D%7B2%7D%5Cleq%5Cfrac%7B2m%7D%7B5%7D%5Ccdot%5Cfrac%7B5%7D%7B2%7D%5Cleq0%5Ccdot%5Cfrac%7B5%7D%7B2%7D%3D%5C%5C%5C%5C%5Cboxed%7B-%5Cfrac%7B5%7D%7B2%7D%5Cleq%5C%2Cm%5Cleq0%7D "\left[\pi,\frac{3\pi}{2}\right]=\\\\\pi\leq\,x\leq\frac{3\pi}{2}=\\\\\cos\pi\leq\cos\,x\leq\cos(\frac{3\pi}{2})=\\\\-1\leq\frac{2m}{5}\leq0=\\\\-1\cdot\frac{5}{2}\leq\frac{2m}{5}\cdot\frac{5}{2}\leq0\cdot\frac{5}{2}=\\\\\boxed{-\frac{5}{2}\leq\,m\leq0}")
Micax:
Muuito obrigada Daniel
Não há de quê!
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