Question

se senx=-1, então o valor de sen5x, é:

Answer 1

$\displaystyle \sin x=-1\iff x\in\left\{\frac{3\pi}{2}+2\pi k:k\in \mathbb Z\right\}$

Entâo

$\displaystyle 5x\in\left\{\frac{15\pi}{2}+2\pi k':k'\in \mathbb Z\right\}\\ \\ \displaystyle 5x\in\left\{\frac{3\pi}{2}+6\pi+2\pi k':k'\in \mathbb Z\right\}\\ \\ \displaystyle 5x\in\left\{\frac{3\pi}{2}+2\pi k'':k''\in \mathbb Z\right\}$

Por ende
                                             $\boxed{\sin 5x = -1}$