Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$
A)
$\begin{array} { l }
\sin x = \frac { 25 } { 24 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
B)
$\begin{array} { l }
\sin x = \frac { 25 } { 7 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
C)
$\begin{array} { l }
\sin x = \frac { 24 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
D)
$\begin{array} { l }
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
E)
$\begin{array} { l }
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$

Question

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$
A)
$\begin{array} { l } 
\sin x = \frac { 25 } { 24 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
B)
$\begin{array} { l } 
\sin x = \frac { 25 } { 7 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
C)
$\begin{array} { l } 
\sin x = \frac { 24 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
D)
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$
E)
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$

Quizplus · Accepted Answer

Given $\csc x = \frac{25}{7}$, we find $\sin x = \frac{1}{\csc x} = \frac{7}{25}$. For $\tan x = \frac{7}{24}$, $\cot x$ being the reciprocal gives $\cot x = \frac{24}{7}$. To find $\cos x$, we use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, leading to $\cos x = \frac{24}{25}$.

Use the Given Values to Evaluate (If Possible) Three Trigonometric csc⁡x=257,tan⁡x=724\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }cscx=725​,tanx=247​

Use the Given Values to Evaluate (If Possible) Three Trigonometric $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$