Use the definitions (not a calculator) to evaluate the six trigonometric functions of the angle. $- 720 ^ { \circ }$
A) $\begin{array} { l l l }
\sin \left( - 720 ^ { \circ } \right) = 1 & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) = 1 \
\cos \left( - 720 ^ { \circ } \right) = 0 & \cot \left( - 720 ^ { \circ } \right) = 0 & \sec \left( - 720 ^ { \circ } \right) \text { is undefined }
\end{array}$
B) $\begin{array} { l l l }
\sin \left( - 720 ^ { \circ } \right) = - 1 & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) = - 1 \
\cos \left( - 720 ^ { \circ } \right) = 0 & \cot \left( - 720 ^ { \circ } \right) = 0 & \sec \left( - 720 ^ { \circ } \right) \text { is undefined }
\end{array}$
C) $\begin{array} { l l l }
\sin \left( - 720 ^ { \circ } \right) = 0 & \tan \left( - 720 ^ { \circ } \right) = 0 & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = - 1 & \cot \left( - 720 ^ { \circ } \right) \text { is undefined } & \sec \left( - 720 ^ { \circ } \right) = - 1
\end{array}$
D) $\begin{array} { l l l }
\sin \left( - 720 ^ { \circ } \right) \text { is undefined } & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = 1 & \cot \left( - 720 ^ { \circ } \right) = 1 & \sec \left( - 720 ^ { \circ } \right) = 1
\end{array}$
E) $\begin{array} { l l l }
\sin \left( - 720 ^ { \circ } \right) = 0 & \tan \left( - 720 ^ { \circ } \right) = 0 & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = 1 & \cot \left( - 720 ^ { \circ } \right) \text { is undefined } & \sec \left( - 720 ^ { \circ } \right) = 1
\end{array}$

Question

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the angle. $- 720 ^ { \circ }$
A) $\begin{array} { l l l } 
\sin \left( - 720 ^ { \circ } \right) = 1 & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) = 1 \
\cos \left( - 720 ^ { \circ } \right) = 0 & \cot \left( - 720 ^ { \circ } \right) = 0 & \sec \left( - 720 ^ { \circ } \right) \text { is undefined }
\end{array}$
B) $\begin{array} { l l l } 
\sin \left( - 720 ^ { \circ } \right) = - 1 & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) = - 1 \
\cos \left( - 720 ^ { \circ } \right) = 0 & \cot \left( - 720 ^ { \circ } \right) = 0 & \sec \left( - 720 ^ { \circ } \right) \text { is undefined }
\end{array}$
C) $\begin{array} { l l l } 
\sin \left( - 720 ^ { \circ } \right) = 0 & \tan \left( - 720 ^ { \circ } \right) = 0 & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = - 1 & \cot \left( - 720 ^ { \circ } \right) \text { is undefined } & \sec \left( - 720 ^ { \circ } \right) = - 1
\end{array}$
D) $\begin{array} { l l l } 
\sin \left( - 720 ^ { \circ } \right) \text { is undefined } & \tan \left( - 720 ^ { \circ } \right) \text { is undefined } & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = 1 & \cot \left( - 720 ^ { \circ } \right) = 1 & \sec \left( - 720 ^ { \circ } \right) = 1
\end{array}$
E) $\begin{array} { l l l } 
\sin \left( - 720 ^ { \circ } \right) = 0 & \tan \left( - 720 ^ { \circ } \right) = 0 & \csc \left( - 720 ^ { \circ } \right) \text { is undefined } \
\cos \left( - 720 ^ { \circ } \right) = 1 & \cot \left( - 720 ^ { \circ } \right) \text { is undefined } & \sec \left( - 720 ^ { \circ } \right) = 1
\end{array}$

Quizplus · Accepted Answer

Rotating $ -720^\circ $ is equivalent to rotating $ 360^\circ $ twice in the negative direction, which brings the angle back to the same position as $ 0^\circ $. At $ 0^\circ $, $\sin(0^\circ) = 0$, $\cos(0^\circ) = 1$, and $\tan(0^\circ) = 0$. The reciprocal functions are undefined for $\sin$ and $\tan$ because you cannot divide by zero, and $\sec(0^\circ) = 1$ because it is the reciprocal of $\cos(0^\circ)$.

Use the Definitions (Not a Calculator) to Evaluate the Six −720∘- 720 ^ { \circ }−720∘

Use the Definitions (Not a Calculator) to Evaluate the Six $- 720 ^ { \circ }$