Use the given values to evaluate (if possible)three trigonometric functions cos x,sin x,cot x. $\tan x = \frac { 9 } { 40 } , \sec x = - \frac { 41 } { 40 }$
A) $\begin{array} { l }
\cos x = \frac { 40 } { 41 } \\
\sin x = \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$
B) $\begin{array} { l }
\cos x = - \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = - \frac { 40 } { 9 }
\end{array}$
C) $\begin{array} { l }
\cos x = - \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$
D) $\begin{array} { l }
\cos x = \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = - \frac { 40 } { 9 }
\end{array}$
E) $\begin{array} { l }
\cos x = - \frac { 40 } { 41 } \\
\sin x = \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$

Question

Use the given values to evaluate (if possible)three trigonometric functions cos x,sin x,cot x.​ $\tan x = \frac { 9 } { 40 } , \sec x = - \frac { 41 } { 40 }$ ​
A) $\begin{array} { l } 
\cos x = \frac { 40 } { 41 } \\
\sin x = \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$ ​
B)​ $\begin{array} { l } 
\cos x = - \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = - \frac { 40 } { 9 }
\end{array}$ ​
C)​ $\begin{array} { l } 
\cos x = - \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$ ​
D)​ $\begin{array} { l } 
\cos x = \frac { 40 } { 41 } \\
\sin x = - \frac { 9 } { 41 } \\
\cot x = - \frac { 40 } { 9 }
\end{array}$ ​
E)​ $\begin{array} { l } 
\cos x = - \frac { 40 } { 41 } \\
\sin x = \frac { 9 } { 41 } \\
\cot x = \frac { 40 } { 9 }
\end{array}$ ​

Quizplus · Accepted Answer

Given $\tan x = \frac{9}{40}$ and $\sec x = -\frac{41}{40}$, we can find $\cos x = \frac{1}{\sec x} = -\frac{40}{41}$. Since $\tan x = \frac{\sin x}{\cos x}$, we can solve for $\sin x = \tan x \cdot \cos x = \frac{9}{40} \cdot -\frac{40}{41} = -\frac{9}{41}$. Finally, $\cot x = \frac{1}{\tan x} = \frac{40}{9}$, which matches the values in option C.

Use the Given Values to Evaluate (If Possible)three Trigonometric Functions tan⁡x=940,sec⁡x=−4140\tan x = \frac { 9 } { 40 } , \sec x = - \frac { 41 } { 40 }tanx=409​,secx=−4041​

Use the Given Values to Evaluate (If Possible)three Trigonometric Functions $\tan x = \frac { 9 } { 40 } , \sec x = - \frac { 41 } { 40 }$