Question

Sendo secx=-3/2 e x€ 2 quadrante, determine senx, cossecx, tgx e cotgx

Answer 1

${ \tan }^{2}x = { \sec }^{2}x - 1 \\ \tan(x) = - \sqrt{ { \sec }^{2}x - 1}$

$\tan(x) = - \sqrt{ {( - \frac{ 3}{4}) }^{2} - 1}$

$\tan(x) = - \sqrt{ \frac{9}{4} - 1 } \\ \tan(x) = - \sqrt{ \frac{9 - 4}{4} }$

$\tan(x) = - \frac{ \sqrt{5} }{ \sqrt{4} } = - \frac{ \sqrt{5} }{2}$

$\cot(x) = - \frac{2}{ \sqrt{5} } = - \frac{2 \sqrt{5} }{5}$

$\sin(x) = \frac{ \tan(x) }{ \sec(x) } \\ \sin(x) = \frac{ \frac{ - \sqrt{5} }{2} }{ - \frac{3}{2} } = \frac{ \sqrt{5} }{3}$

$\csc(x) = \frac{3}{ \sqrt{5} } = \frac{3 \sqrt{5} }{5}$