Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & & \frac { \pi } { 3 } & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \text { sec } & 45 ^ { \circ } & \frac { \pi } { 3 } & \sqrt { 2 } \
\hline
\end{array}$$
B)?$$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { sec } & 90 ^ { \circ } & \frac { \pi } { 3 } & \text { Not defined } \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 60 ^ { \circ } & \frac { \pi } { 3 } & 2 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 0 ^ { \circ } & \frac { \pi } { 3 } & 1 \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | }
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 30 ^ { \circ } & \frac { \pi } { 3 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Question

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & & \frac { \pi } { 3 } & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \text { sec } & 45 ^ { \circ } & \frac { \pi } { 3 } & \sqrt { 2 } \
\hline
\end{array}$$
B)?$$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { sec } & 90 ^ { \circ } & \frac { \pi } { 3 } & \text { Not defined } \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 60 ^ { \circ } & \frac { \pi } { 3 } & 2 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 0 ^ { \circ } & \frac { \pi } { 3 } & 1 \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 30 ^ { \circ } & \frac { \pi } { 3 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Quizplus · Accepted Answer

$\theta = \frac{\pi}{3}$ radians is equivalent to $60^\circ$. The secant function, $\sec(\theta)$, is the reciprocal of the cosine function. For $\theta = 60^\circ$, $\cos(60^\circ) = \frac{1}{2}$, so $\sec(60^\circ) = \frac{1}{\cos(60^\circ)} = 2$.

Construct an Appropriate Triangle to Complete the Table (0∘≤θ≤90∘,0∘≤θ≤π2)\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)(0∘≤θ≤90∘,0∘≤θ≤2π​)

Construct an Appropriate Triangle to Complete the Table $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$