Question

Trigometria - Foto abaixo
Sabendo que cos π/3 = 1/2, qual valor de cos 2π/3 de 4π/3 e cos 5π/3?

Answer 1

Explicação passo-a-passo:

=> $\sf cos~\Big(\dfrac{2\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{2\pi}{3}\Big)=-cos~\Big(\pi-\dfrac{2\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{2\pi}{3}\Big)=-cos~\Big(\dfrac{3\pi-2\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{2\pi}{3}\Big)=-cos~\Big(\dfrac{\pi}{3}\Big)$

$\sf \red{cos~\Big(\dfrac{2\pi}{3}\Big)=-\dfrac{1}{2}}$

=> $\sf cos~\Big(\dfrac{4\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{4\pi}{3}\Big)=-cos\Big(\dfrac{4\pi}{3}-\pi\Big)$

$\sf cos~\Big(\dfrac{4\pi}{3}\Big)=-cos\Big(\dfrac{4\pi-3\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{4\pi}{3}\Big)=-cos\Big(\dfrac{\pi}{3}\Big)$

$\sf \red{cos~\Big(\dfrac{4\pi}{3}\Big)=-\dfrac{1}{2}}$

=> $\sf cos~\Big(\dfrac{5\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{5\pi}{3}\Big)=cos~\Big(2\pi-\dfrac{5\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{5\pi}{3}\Big)=cos~\Big(\dfrac{6\pi-5\pi}{3}\Big)$

$\sf cos~\Big(\dfrac{5\pi}{3}\Big)=cos~\Big(\dfrac{\pi}{3}\Big)$

$\sf \red{cos~\Big(\dfrac{5\pi}{3}\Big)=\dfrac{1}{2}}$