Question

Calcular o valor de cotg 37pi/6, sec 37pi/6 e cossec 37pi/6 ?

me ajudem por favooooooooor !

Answer 1

Olá, Bibi.

$\frac{37\pi}6=\frac{\pi}6+\frac{36\pi}6=\frac{\pi}6+6\pi=\frac{\pi}6+3\cdot2\pi\Rightarrow \frac{37\pi}6\equiv\frac{\pi}6\\\\ \cot\frac{37\pi}6=\cot\frac{\pi}6=(\text{tg }\frac{\pi}6)^{-1}=(\text{tg }30\º)^{-1}=(\frac{\sqrt3}{3})^{-1}=\frac3{\sqrt3}=\frac{3\sqrt3}{3}=\sqrt3\\\\ \sec\frac{37\pi}6=\sec\frac{\pi}6=(\cos\frac{\pi}6)^{-1}=(\cos30\º)^{-1}=(\frac{\sqrt3}{2})^{-1}=\frac2{\sqrt3}=\frac{2\sqrt3}{3}$

$\text{cossec }\frac{37\pi}6=\text{cossec }\frac{\pi}6=(\text{sen }\frac{\pi}6)^{-1}=(\text{sen }30\º)^{-1}=(\frac12)^{-1}=2$