Question

Valores trigonométricos de ângulos especiais cos( 4π/3) e sen( 4π/3)

Answer 1

Para qualquer x real valem as igualdades 

$\cos{x}=-\cos{(x-\pi)}\\ \sin{x}=-\sin{(x-\pi)}$

Logo

$\displaystyle \cos{\left(\frac{4\pi}{3}\right)}=-\cos{\left(\frac{4\pi}{3}-\pi\right)}=-\cos{\left(\frac{\pi}{3}\right)=-\frac{1}{2}}\\\\\\ \sin{\left(\frac{4\pi}{3}\right)}=-\sin{\left(\frac{4\pi}{3}-\pi\right)}=-\sin{\left(\frac{\pi}{3}\right)}=-\frac{\sqrt{3}}{2}$