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

The tangent function is the reciprocal of the cotangent function, so $\tan \varphi = -\frac{1}{5}$ given $\cot \varphi = -5$. The cosecant function is the reciprocal of the sine function, so $\csc \psi = \frac{1}{\sin \psi} = \sqrt{10}$ given $\sin \psi = \frac{\sqrt{10}}{10}$.

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