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

Question

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

Quizplus · Accepted Answer

The tangent function ($\tan$) is not defined at $\theta = 90^\circ$ or $\theta = \frac{\pi}{2}$ radians because at this angle, the function approaches infinity, indicating a vertical line where the cosine of the angle is zero, making the tangent undefined.

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 $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$