Question

seja x o arco do 3º quadrante e sen x = - 1/2
a) cos(x)
b) cos (2x)

Answer 1

$\boxed{\mathsf{ sen^{2}(x) +cos^{2}(x) = 1 }} \\ cos(x) = \pm \sqrt{1 -(-\frac{1}{2})^{2}} \\ cos(x) = \pm \sqrt{\frac{3}{4} } \\ cos(x) = \pm \frac{\sqrt{3} }{2} \to 3^{o}Q \to -\frac{\sqrt{3} }{2} \\ \\ \\ \boxed{\mathsf{ cos(2x) = 2cos^{2}(x) -1}} \\ cos(2x)=2 * (-\frac{\sqrt{3} }{2} )^{2} -1 \\ cos(2x) = 2 * \frac{3}{4} -1 \\ cos(2x) = \frac{3}{2} -1 \\ cos(2x) = \frac{1}{2}$