Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x.
$\cos \left( \frac { \pi } { 2 } - x \right) = \frac { 8 } { 17 } , \cos x = \frac { 15 } { 17 }$
A) $\begin{array} { l }
\csc x = - \frac { 8 } { 5 } \
\tan x = - \frac { 8 } { 15 } \
\cot x = - \frac { 15 } { 8 }
\end{array}$
B) $\begin{array} { l }
\csc x = - \frac { 15 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$
C) $\begin{array} { l }
\csc x = \frac { 15 } { 8 } \
\tan x = - \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$
D) $\begin{array} { l }
\csc x = \frac { 17 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$
E) $\begin{array} { l }
\csc x = \frac { 5 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = - \frac { 15 } { 8 }
\end{array}$

Question

Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x. 
 $\cos \left( \frac { \pi } { 2 } - x \right) = \frac { 8 } { 17 } , \cos x = \frac { 15 } { 17 }$  
A)  $\begin{array} { l } 
\csc x = - \frac { 8 } { 5 } \
\tan x = - \frac { 8 } { 15 } \
\cot x = - \frac { 15 } { 8 }
\end{array}$  
B)  $\begin{array} { l } 
\csc x = - \frac { 15 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$  
C)  $\begin{array} { l } 
\csc x = \frac { 15 } { 8 } \
\tan x = - \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$  
D)  $\begin{array} { l } 
\csc x = \frac { 17 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = \frac { 15 } { 8 }
\end{array}$  
E)  $\begin{array} { l } 
\csc x = \frac { 5 } { 8 } \
\tan x = \frac { 8 } { 15 } \
\cot x = - \frac { 15 } { 8 }
\end{array}$

Quizplus · Accepted Answer

Given $\cos \left( \frac { \pi } { 2 } - x \right) = \frac { 8 } { 17 }$, this is equivalent to $\sin x = \frac { 8 } { 17 }$ because $\cos \left( \frac { \pi } { 2 } - x \right) = \sin x$. With $\cos x = \frac { 15 } { 17 }$, we can find the other trigonometric functions. $\csc x = \frac { 1 } { \sin x } = \frac { 17 } { 8 }$, $\tan x = \frac { \sin x } { \cos x } = \frac { 8 } { 15 }$, and $\cot x = \frac { 1 } { \tan x } = \frac { 15 } { 8 }$.

Use the Given Values to Evaluate (If Possible) Three Trigonometric cos⁡(π2−x)=817,cos⁡x=1517\cos \left( \frac { \pi } { 2 } - x \right) = \frac { 8 } { 17 } , \cos x = \frac { 15 } { 17 }cos(2π​−x)=178​,cosx=1715​

Use the Given Values to Evaluate (If Possible) Three Trigonometric $\cos \left( \frac { \pi } { 2 } - x \right) = \frac { 8 } { 17 } , \cos x = \frac { 15 } { 17 }$