Question

*URGENTE* Seja β E [ - π, - π/2] tal que cos β = -0, 6. Determine se existir
A) sen β
B) cos β
C) tg β
D) cotg β
E) sec β
F) cossec β

Answer 1

Explicação passo-a-passo:

A) sen β

$\sin ^{2} \beta + \cos^{2} \beta = 1 \\ \sin ^{2} \beta = 1 - {(-0.6)} ^{2} \\ \sin ^{2} \beta = 1 -0 .36 \\ \sin ^{2} \beta= 0.64 \\ \sin( \beta ) = \sqrt{0.64} = 0.8$

B) cos β = 0,6

C) tg β

$\tan( \beta ) = \frac{ \sin( \beta ) }{ \cos( \beta ) } = \frac{0.8}{-0.6} = - 1.333$

D) cotg β

$\cot( \beta ) = \frac{ \cos( \beta ) }{ \sin( \beta ) } = \frac{-0.6}{0.8} = - 0.75$

E) sec β

$\sec( \beta ) = \frac{1}{ \cos( \beta ) } = \frac{1}{-0.6} = - 1.666$

F) cossecβ

$\csc( \beta ) = \frac{1}{ \sin( \beta ) } = \frac{1}{0.8} = 1.25$