Use the given values to evaluate (if possible)three trigonometric functions $\cos \phi , \sin \phi , \tan \phi$ . $\sec \phi = \frac { 3 } { 4 } , \csc \phi = \frac { - 3 \sqrt { 5 } } { 5 }$
A) $\begin{array} { l }
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = \frac { \sqrt { 5 } } { 4 }
\end{array}$
B) $\begin{array} { l }
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$
C) $\begin{array} { l }
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$
D) $\begin{array} { l }
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = \frac { \sqrt { 5 } } { 3 } \
\tan \phi = \frac { \sqrt { 5 } } { 4 }
\end{array}$
E) $\begin{array} { l }
\cos \phi = - \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$

Question

Use the given values to evaluate (if possible)three trigonometric functions $\cos \phi , \sin \phi , \tan \phi$ .​ $\sec \phi = \frac { 3 } { 4 } , \csc \phi = \frac { - 3 \sqrt { 5 } } { 5 }$ ​
A)​ $\begin{array} { l } 
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = \frac { \sqrt { 5 } } { 4 }
\end{array}$ ​
B)​ $\begin{array} { l } 
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$ ​
C)​ $\begin{array} { l } 
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$ ​
D)​ $\begin{array} { l } 
\cos \phi = \frac { 4 } { 3 } \
\sin \phi = \frac { \sqrt { 5 } } { 3 } \
\tan \phi = \frac { \sqrt { 5 } } { 4 }
\end{array}$ ​
E)​ $\begin{array} { l } 
\cos \phi = - \frac { 4 } { 3 } \
\sin \phi = - \frac { \sqrt { 5 } } { 3 } \
\tan \phi = - \frac { \sqrt { 5 } } { 4 }
\end{array}$

Quizplus · Accepted Answer

The correct values are derived from the given secant and cosecant values. The secant ($\sec \phi$) is the reciprocal of the cosine ($\cos \phi$), so $\cos \phi = \frac{1}{\sec \phi} = \frac{1}{\frac{3}{4}} = \frac{4}{3}$. The cosecant ($\csc \phi$) is the reciprocal of the sine ($\sin \phi$), so $\sin \phi = \frac{1}{\csc \phi} = \frac{1}{\frac{-3\sqrt{5}}{5}} = -\frac{\sqrt{5}}{3}$. The tangent ($\tan \phi$) is the sine divided by the cosine, so $\tan \phi = \frac{\sin \phi}{\cos \phi} = \frac{-\frac{\sqrt{5}}{3}}{\frac{4}{3}} = -\frac{\sqrt{5}}{4}$.

Use the Given Values to Evaluate (If Possible)three Trigonometric Functions cos⁡ϕ,sin⁡ϕ,tan⁡ϕ\cos \phi , \sin \phi , \tan \phicosϕ,sinϕ,tanϕ

Use the Given Values to Evaluate (If Possible)three Trigonometric Functions $\cos \phi , \sin \phi , \tan \phi$