Question

Utilizando simetria e sabendo que sen π/6 = 1/2 , dê o valor de seno 5π/6 , 7π/6 e 11π/6

50 PONTOS MEE AJUDEM

Answer 1

Explicação passo-a-passo:

a)

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

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

$\sf sen~\Big(\dfrac{5\pi}{6}\Big)=sen~\Big(\dfrac{\pi}{6}\Big)$

$\sf \red{sen~\Big(\dfrac{5\pi}{6}\Big)=\dfrac{1}{2}}$

b)

$\sf sen~\Big(\dfrac{7\pi}{6}\Big)=-sen~\Big(\dfrac{7\pi}{6}-\pi\Big)$

$\sf sen~\Big(\dfrac{7\pi}{6}\Big)=-sen~\Big(\dfrac{7\pi-6\pi}{6}\Big)$

$\sf sen~\Big(\dfrac{7\pi}{6}\Big)=-sen~\Big(\dfrac{\pi}{6}\Big)$

$\sf \red{sen~\Big(\dfrac{7\pi}{6}\Big)=-\dfrac{1}{2}}$

c)

$\sf sen~\Big(\dfrac{11\pi}{6}\Big)=-sen~\Big(2\pi-\dfrac{11\pi}{6}\Big)$

$\sf sen~\Big(\dfrac{11\pi}{6}\Big)=-sen~\Big(\dfrac{12\pi-11\pi}{6}\Big)$

$\sf sen~\Big(\dfrac{11\pi}{6}\Big)=-sen~\Big(\dfrac{\pi}{6}\Big)$

$\sf \red{sen~\Big(\dfrac{11\pi}{6}\Big)=-\dfrac{1}{2}}$