Evaluate (if possible) the sine, cosec, and tangent of the real number. $t = - 8 \pi$
A) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l }
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) \text { is undefined } \
\tan ( - 8 \pi ) = 0
\end{array}$
B) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l }
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
C) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l }
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
D) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l }
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
E)Not possible

Question

Evaluate (if possible) the sine, cosec, and tangent of the real number.   $t = - 8 \pi$  
A) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) \text { is undefined } \
\tan ( - 8 \pi ) = 0
\end{array}$
B) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
C) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
D) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$
E)Not possible

Quizplus · Accepted Answer

The angle $t = -8\pi$ represents a full rotation of $2\pi$ radians, repeated four times in the negative direction. This brings the point back to $(1,0)$ on the unit circle, where $\sin(-8\pi) = 0$, $\csc(-8\pi)$ is undefined because $\csc$ is the reciprocal of sine and you cannot divide by zero, and $\tan(-8\pi) = 0$ because tangent is sine over cosine, and here sine is 0.

Evaluate (If Possible) the Sine, Cosec, and Tangent of the Real