Question

Calcule a expressão:

2/3 sen + pi/2 + 3/5 sen 5pi/3 -6/7 sen 7pi/6

Answer 1

Resposta:

pi.mi -45pi resultado completo

Answer 2

Resposta:

Explicação passo-a-passo:

Temos que:

i) sen $\frac{\pi}{2}=1$, logo, $\frac{2}{3}.sen\frac{\pi}{2}=\frac{2}{3}.1=\frac{2}{3}$

ii) $sen\frac{5\pi}{3}=sen5.60^{0}=sen300^{0}=-sen60^{0}=-\frac{\sqrt{3}}{2}$. Portanto, $\frac{3}{5}sen\frac{5\pi}{3}=\frac{3}{5}.(-\frac{\sqrt{3}}{2})=-\frac{3\sqrt{3}}{10}$

iii) $sen\frac{7\pi}{6}=sen210^{0}=-sen30^{0}=-\frac{1}{2}$. Portanto, $-\frac{6}{7}sen\frac{7\pi}{6}=-\frac{6}{7}.(-\frac{1}{2})=\frac{3}{7}$.

Assim:

$\frac{2}{3}sen\frac{\pi}{2}+\frac{3}{5}sen\frac{5\pi}{3}-\frac{6}{7}sen\frac{7\pi}{6}=\frac{2}{3}-\frac{3\sqrt{3}}{10}+\frac{3}{7}=\frac{70.2-21.3\sqrt{3}+30.3}{210}=\frac{140-63\sqrt{3}+90}{210}=\frac{230-63\sqrt{3}}{210}$