Question

Calcule m sabendo que sen x = m cos x = -m​

Answer 1

$\displaystyle \sf \text{Rela{\c c}{\~a}o Fundamental da trigonometria } : \\\\ sen^2 x+cos^2 x= 1 \\\\ temos : \\\\ sen \ x = m \ \ , \ \ cos\ x = -m \\\\ Da{\'i}}: \\\\ m^2+(-m)^2 = 1 \to m^2+m^2 = 1\\\\ 2m^2 = 1 \to m^2 = \frac{1}{2} \\\\ m =\pm \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \\\\\\ portanto : \\\\ \boxed{\begin{array}{I} \displaystyle \sf m =\frac{\sqrt{2}}{2}\\\\ \displaystyle \sf ou \\\\\ \displaystyle \sf m = \frac{-\sqrt{2}}{2} \end{array}}\checkmark$