Question

Sendo senx=-3/4, com π< x< 3π/2 determine a tgx e secantgx

Answer 1

Sen²x + Cos²x = 1
(-3/4)² + Cos²x = 1
9/16 + Cos²x = 1
Cos²x = 1 - 9/16
Cos²x = 16-9/16
Cos²x = 7/16
Cosx = √7/4

Portanto, tg(x) = Sen(x)/Cos(x) = $\frac{\frac{-3}{4} }{\frac{\sqrt{7} } {4} } = \frac{-3}{4} .\frac{4}{\sqrt{7} } = \frac{-3\sqrt{7} }{7}$

Secante(x) = 1/cos(x) = $\frac{1}{ \frac{\sqrt{7} }{4} } = \frac{4\sqrt{7} }{7}$