Question

Dado senx=- √3/2, com 270° < x < 360°

. Determine cosx, tgx, sectx, cossectx e cotgx.​

Answer 1

$\dfrac{3\pi}{2}<x<2\pi$

$\boxed{\sin{x}=-\dfrac{\sqrt{3}}{2}}$

$\sin^2{x}+\cos^2{x}=1\ \therefore\ \cos{x}=\pm\sqrt{1-\dfrac{3}{4}}\ \therefore\ \cos{x}=\pm\dfrac{1}{2}$

$\dfrac{3\pi}{2}<x<2\pi\ \therefore\ \boxed{\cos{x}=\dfrac{1}{2}}$

$\tan{x}=\dfrac{\sin{x}}{\cos{x}}=-\dfrac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\ \therefore\ \boxed{\tan{x}=-\sqrt{3}}$

$\csc{x}=\dfrac{1}{\sin{x}}=-\dfrac{1}{\frac{\sqrt{3}}{2}}=-\dfrac{2}{\sqrt{3}}\ \therefore\ \boxed{\csc{x}=-\dfrac{2\sqrt{3}}{3}}$

$\sec{x}=\dfrac{1}{\cos{x}}=\dfrac{1}{\frac{1}{2}}\ \therefore\ \boxed{\sec{x}=2}$

$\cot{x}=\dfrac{1}{\tan{x}}=-\dfrac{1}{\sqrt{3}}\ \therefore\ \boxed{\cot{x}=-\dfrac{\sqrt{3}}{3}}$