Question

a relação fundamental da trigonometria é sen2×+cos2×=1. dado o Sena =1/2, podemos afirmar que cosx é?​

Answer 1

Temos $sen^2\alpha+cos^2\alpha=1$ e que $sen\alpha=\dfrac{1}{2}$, então

$\overbrace{sen^2\alpha}^{\dfrac{1}{2}}+cos^2\alpha=1\\\\\left(\dfrac{1}{2}\right)^2+cos^2\alpha=1\\\\\dfrac{1}{4}+cos^2\alpha=1\\\\cos^2\alpha=1-\dfrac{1}{4}\\\\cos^2\alpha=\dfrac{4-1}{4}\\\\cos^2\aplha=\dfrac{3}{4}\\\\cos\alpha=\pm\sqrt{\dfrac{3}{4}}\\\\cos\alpha=\pm\dfrac{\sqrt{3}}{\sqrt{4}}\\\\\boxed{\boxed{cos\alpha=\pm\dfrac{\sqrt{3}}{2}}}$