One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\sin x = - \frac { 1 } { 5 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$
A) $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$
B) $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$
C) $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$
D) $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$

Question

Quizplus · Accepted Answer

Given $\sin x = -\frac{1}{5}$ and $x$ is in the interval $\left[-\frac{\pi}{2}, 0\right]$, the cosine of $x$ must be positive because cosine is positive in the fourth quadrant. Using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, we find $\cos x = \frac{2\sqrt{6}}{5}$. The tangent, $\tan x = \frac{\sin x}{\cos x}$, is negative because $\sin x$ is negative and $\cos x$ is positive, giving $\tan x = -\frac{\sqrt{6}}{12}$.

One of Sin X, Cos X, and Tan X Is sin⁡x=−15,x\sin x = - \frac { 1 } { 5 } , \quad xsinx=−51​,x

One of Sin X, Cos X, and Tan X Is $\sin x = - \frac { 1 } { 5 } , \quad x$