Question

Sabendo que sen(x)= √m/2 e cos(x)= √m-2/2, calcule o valor de m vale:

A) 1
B) 2
C) 3
D) 4
E) 8

Answer 1

Boa tarde!


Solução!


$Sen(x)= \dfrac{ \sqrt{m} }{2}\\\\\\\\ cos(x)= \dfrac{ \sqrt{m-2} }{2}\\\\\\\\ Aplicando~~a~~relac\~ao~~fundamental~~da~~trigonometria.\\\\\\\\ Sen^{2}(x)+Cos^{2}x=1$



$\left ( \dfrac{ \sqrt{m} }{2} \right )^{2}+ \left ( \dfrac{ \sqrt{m-2} }{2} \right )^{2}=1\\\\\\\\\\\ \left ( \dfrac{ m }{4} \right )+ \left ( \dfrac{ m-2 }{4} \right )=1\\\\\\\\\\\ \left ( \dfrac{ m }{4} +\dfrac{ m-2 }{4} \right )=1\\\\\\\\\\\ m+m-2=4\\\\\\ 2m=4+2\\\\\\ 2m=6\\\\\\ m= \dfrac{6}{2}\\\\\\ \boxed{m=3}$


$\boxed{m=3~~\boxed{Resposta:Alternativa~~C~}}$


Boa tarde!
Bons estudos!