Trigonometria

por FISMAQUI Sex 03 Set 2021, 08:04

Econtre o valor de x, sabendo que [latex]arcsen\left ( cos\frac{83\Pi }{4} \right ) = x[/latex].

por **Victor011** Sex 03 Set 2021, 08:58

Olá FISMAQUI! Trigonometria 1f600

[latex]\\\frac{83\pi}{4}=\frac{84\pi}{4}-\frac{\pi}{4}=21\pi-\frac{\pi}{4}=20\pi+\frac{3\pi}{4}\\\\ \rightarrow\;\cos\frac{83\pi}{4}=\cos\left (20\pi+\frac{3\pi}{4}\right )=\cos\left (\frac{3\pi}{4}\right )=-\frac{\sqrt{2}}{2}\\\\ \rightarrow\;x=\arcsin\left ( -\frac{\sqrt{2}}{2}\right )\\\\ \rightarrow\;\boxed{x=\frac{5\pi}{4}+2k\pi\;\;\text{ou}\;\;x=\frac{7\pi}{4}+2k\pi}\;,\;\;\forall k\in\mathbb{Z}[/latex]