One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$
A) $\cos x = \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$
B) $\cos x = - 2 , \tan x = \frac { \sqrt { 3 } } { 3 }$
C) $\cos x = \frac { 1 } { 2 } , \tan x = \sqrt { 3 }$
D) $\cos x = - \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$

Question

Quizplus · Accepted Answer

Since $\sin x = -\frac{\sqrt{3}}{2}$ and $x\in \left[-\frac{\pi}{2},0ight],$ we know that $x$ is in the third quadrant where the sine function is negative. Drawing a $30^\circ$-$60^\circ$-$90^\circ$ triangle in the third quadrant, we have $\cos x = \frac{1}{2}$ and $	an x = \frac{\sin x}{\cos x} = -\sqrt{3}.$ Thus, the answer is $\boxed{	extbf{(A)}}.$

One of Sin X, Cos X, and Tan X Is sin⁡x=−32,x\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad xsinx=−23​​,x

One of Sin X, Cos X, and Tan X Is $\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x$