Use the given values to evaluate (if possible) two trigonometric functions $\tan \varphi$ and $\csc \psi$ .
$\cot \varphi = - 5 , \sin \psi = \frac { \sqrt { 10 } } { 10 }$
A) $\begin{array} { l }
\tan \varphi = - \frac { 1 } { 5 } \
\csc \psi = \sqrt { 10 }
\end{array}$
B) $\begin{array} { l }
\tan \varphi = \frac { 1 } { 5 } \
\csc \psi = \sqrt { 10 }
\end{array}$
C) $\begin{array} { l }
\tan \varphi = \frac { 1 } { 5 } \
\csc \psi = - \sqrt { 10 }
\end{array}$
D) $\begin{array} { l }
\tan \varphi = - 5 \
\csc \psi = \sqrt { 10 }
\end{array}$
E) $\begin{array} { l }
\tan \varphi = - \frac { 1 } { 5 } \
\csc \psi = - \sqrt { 10 }
\end{array}$

Question

Use the given values to evaluate (if possible) two trigonometric functions $\tan \varphi$ and $\csc \psi$ . 
 $\cot \varphi = - 5 , \sin \psi = \frac { \sqrt { 10 } } { 10 }$  
A)  $\begin{array} { l } 
\tan \varphi = - \frac { 1 } { 5 } \
\csc \psi = \sqrt { 10 }
\end{array}$  
B)  $\begin{array} { l } 
\tan \varphi = \frac { 1 } { 5 } \
\csc \psi = \sqrt { 10 }
\end{array}$  
C)  $\begin{array} { l } 
\tan \varphi = \frac { 1 } { 5 } \
\csc \psi = - \sqrt { 10 }
\end{array}$  
D)  $\begin{array} { l } 
\tan \varphi = - 5 \
\csc \psi = \sqrt { 10 }
\end{array}$  
E)  $\begin{array} { l } 
\tan \varphi = - \frac { 1 } { 5 } \
\csc \psi = - \sqrt { 10 }
\end{array}$

Quizplus · Accepted Answer

$\tan \varphi = -\frac{1}{5}$ because $\tan \varphi = \frac{1}{\cot \varphi} = \frac{1}{-5}$. $\csc \psi = \sqrt{10}$ because $\csc \psi = \frac{1}{\sin \psi} = \frac{1}{\sqrt{10}/10} = \sqrt{10}$.

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Use the Given Values to Evaluate (If Possible) Two Trigonometric $\tan \varphi$