Use the given values to evaluate (if possible) three trigonometric functions cos x, sin x, tan x.
$\sec x = 4 , \sin x 0$

A) $\begin{array} { l }
\cos x = \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$
B) $\begin{array} { l }
\cos x = \frac { 1 } { 4 } \
\sin x = \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$
C) $\begin{array} { l }
\cos x = \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = - \sqrt { 15 }
\end{array}$
D) $\begin{array} { l }
\cos x = - \frac { 1 } { 4 } \
\sin x = \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$
E) $\begin{array} { l }
\cos x = - \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = - \sqrt { 15 }
\end{array}$

Question

Use the given values to evaluate (if possible) three trigonometric functions cos x, sin x, tan x. 
 $\sec x = 4 , \sin x > 0$  
 
A)  $\begin{array} { l } 
\cos x = \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$  
B)  $\begin{array} { l } 
\cos x = \frac { 1 } { 4 } \
\sin x = \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$  
C)  $\begin{array} { l } 
\cos x = \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = - \sqrt { 15 }
\end{array}$  
D)  $\begin{array} { l } 
\cos x = - \frac { 1 } { 4 } \
\sin x = \frac { \sqrt { 15 } } { 4 } \
\tan x = \sqrt { 15 }
\end{array}$  
E)  $\begin{array} { l } 
\cos x = - \frac { 1 } { 4 } \
\sin x = - \frac { \sqrt { 15 } } { 4 } \
\tan x = - \sqrt { 15 }
\end{array}$

Quizplus · Accepted Answer

Given $\sec x = 4$, we find $\cos x = \frac{1}{\sec x} = \frac{1}{4}$. Since $\sin x > 0$ and using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, we calculate $\sin x = \frac{\sqrt{15}}{4}$. The tangent is the ratio of sine over cosine, giving $\tan x = \frac{\sin x}{\cos x} = \sqrt{15}$.

Use the Given Values to Evaluate (If Possible) Three Trigonometric sec⁡x=4,sin⁡x>0\sec x = 4 , \sin x > 0secx=4,sinx>0

Use the Given Values to Evaluate (If Possible) Three Trigonometric $\sec x = 4 , \sin x > 0$