Question 1

Use a calculator to evaluate $\csc \left( \frac { \pi } { 10 } \right)$ .Round your answer to four decimal places.

Accepted Answer

A) -1.8382 
B) -24.0997 
C) 0.3090 
D) 3.2361 
E) -0.0415 
A) -1.8382 
B) -24.0997 
C) 0.3090 
D) 3.2361 
E) -0.0415

Question 2

Evaluate each function.Round your answers to four decimal places. ​
Cos17°36' and sin67°23'
​

Accepted Answer

A) 1.0032 and 0.9731 
B) 1.0532 and 1.0231 
C) 1.1532 and 1.1231 
D) 1.1032 and 1.0731 
E) 0.9532 and 0.9231 
A) 1.0032 and 0.9731 
B) 1.0532 and 1.0231 
C) 1.1532 and 1.1231 
D) 1.1032 and 1.0731 
E) 0.9532 and 0.9231

Question 3

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. )

Accepted Answer

A) sin ? = $$\frac { 85 } { 13 }$$ csc ? = $\frac { 13 } { 85 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 84 } { 85 }$
Tan ? = $\frac { 84 } { 13 }$
Cot ? = $\frac { 13 } { 84 }$
? 
B) sin ? = $\frac { 84 } { 13 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 84 } { 85 }$
? 
C) sin ? = $\frac { 84 } { 85 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 13 } { 85 }$
Sec ? = $\frac { 84 } { 13 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 85 } { 84 }$
? 
D) sin ? = $\frac { 85 } { 84 }$ csc ? = $$\frac { 85 } { 13 }$$
Cos ? = $$\frac { 84 } { 13 }$$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 85 }$
? 
E) sin ? = $\frac { 13 } { 85 }$ csc ? = $\frac { 85 } { 13 }$
Cos ? = $\frac { 84 } { 85 }$
Sec ? = $\frac { 85 } { 84 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 13 }$
? 
A) sin ? = $$\frac { 85 } { 13 }$$ csc ? = $\frac { 13 } { 85 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 84 } { 85 }$
Tan ? = $\frac { 84 } { 13 }$
Cot ? = $\frac { 13 } { 84 }$
? 
B) sin ? = $\frac { 84 } { 13 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 84 } { 85 }$
? 
C) sin ? = $\frac { 84 } { 85 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 13 } { 85 }$
Sec ? = $\frac { 84 } { 13 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 85 } { 84 }$
? 
D) sin ? = $\frac { 85 } { 84 }$ csc ? = $$\frac { 85 } { 13 }$$
Cos ? = $$\frac { 84 } { 13 }$$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 85 }$
? 
E) sin ? = $\frac { 13 } { 85 }$ csc ? = $\frac { 85 } { 13 }$
Cos ? = $\frac { 84 } { 85 }$
Sec ? = $\frac { 85 } { 84 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 13 }$
?

Question 4

Evaluate each function.Round your answers to four decimal places.? $\sec \left( \frac { \pi } { 2 } - 2 \right)$ and $\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)$ ?

Accepted Answer

A) 1.1998 and 0.4463 
B) 1.2998 and 0.5463 
C) 1.1498 and 0.3963 
D) 1.0998 and 0.3463 
E) 1.2498 and 0.4963 
A) 1.1998 and 0.4463 
B) 1.2998 and 0.5463 
C) 1.1498 and 0.3963 
D) 1.0998 and 0.3463 
E) 1.2498 and 0.4963

Question 5

Evaluate each function.Round your answers to four decimal places. ​
Sin22.3° and csc22.3°
​

Accepted Answer

A) 0.5795 and 2.8354 
B) 0.3795 and 2.6354 
C) 0.4795 and 2.7354 
D) 0.4295 and 2.6854 
E) 0.5295 and 2.7854 
A) 0.5795 and 2.8354 
B) 0.3795 and 2.6354 
C) 0.4795 and 2.7354 
D) 0.4295 and 2.6854 
E) 0.5295 and 2.7854

Question 6

Complete the table. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & & & & & \
\hline
\end{array}$$
(Round your answer to four decimal places. )

Accepted Answer

A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7833 & 0.8415 & 0.8912 & 0.932 \
\hline
\end{array}$$ 
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0 & 1 & 2 & 3 & 4 \
\hline
\end{array}$$ 
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.932 & 0.8912 & 0.8415 & 0.7833 & 0.7174 \
\hline
\end{array}$$ 
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7174 & 0.8415 & 0.7174 & 0.932 \
\hline
\end{array}$$ 
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline
\end{array}$$ 
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7833 & 0.8415 & 0.8912 & 0.932 \
\hline
\end{array}$$ 
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0 & 1 & 2 & 3 & 4 \
\hline
\end{array}$$ 
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.932 & 0.8912 & 0.8415 & 0.7833 & 0.7174 \
\hline
\end{array}$$ 
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7174 & 0.8415 & 0.7174 & 0.932 \
\hline
\end{array}$$ 
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline
\end{array}$$

Question 7

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. ?sin ? = 1 and csc ? = 1
?
?

Accepted Answer

A) 90° = $\frac { \pi } { 2 }$ 
B) ?30° = $\frac { \pi } { 6 }$ 
C) ?0° = 0 
D) ?60° = $\frac { \pi } { 3 }$ 
E) ?45° = $\frac { \pi } { 4 }$ 
A) 90° = $\frac { \pi } { 2 }$ 
B) ?30° = $\frac { \pi } { 6 }$ 
C) ?0° = 0 
D) ?60° = $\frac { \pi } { 3 }$ 
E) ?45° = $\frac { \pi } { 4 }$

Question 8

Evaluate each function.Round your answers to four decimal places. ​
Sec48°38' and csc31°57'
​

Accepted Answer

A) 1.7131 and 2.0897 
B) 1.6131 and 1.9897 
C) 1.5631 and 1.9397 
D) 1.5131 and 1.8897 
E) 1.6631 and 2.0397 
A) 1.7131 and 2.0897 
B) 1.6131 and 1.9897 
C) 1.5631 and 1.9397 
D) 1.5131 and 1.8897 
E) 1.6631 and 2.0397

Question 9

Using trigonometric identities,determine which of the following is equivalent to the following expression. ?
Tan ? + cot ?   ?

Accepted Answer

A) ?1 
B) ?csc ? sec ? 
C)  $\mathrm { csc }$ ? ? + $\sin$ ? 
D) ?cos ? + sec ? 
E) ?sec ? + csc ? 
A) ?1 
B) ?csc ? sec ? 
C)  $\mathrm { csc }$ ? ? + $\sin$ ? 
D) ?cos ? + sec ? 
E) ?sec ? + csc ?

Question 10

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. sec ? = $\sqrt { 2 }$ and cot ? = 1
?
?

Accepted Answer

A) 45° = $\frac { \pi } { 4 }$ 
B) ?90° = $\frac { \pi } { 2 }$ 
C) ?0° = 0 
D) ?60° = $\frac { \pi } { 3 }$ 
E) ?30° = $\frac { \pi } { 6 }$ 
A) 45° = $\frac { \pi } { 4 }$ 
B) ?90° = $\frac { \pi } { 2 }$ 
C) ?0° = 0 
D) ?60° = $\frac { \pi } { 3 }$ 
E) ?30° = $\frac { \pi } { 6 }$

Question 11

Evaluate each function.Round your answers to four decimal places. ​
Sec0.74 and cos0.74
​

Accepted Answer

A) 1.4042 and 0.7885 
B) 1.5542 and 0.9385 
C) 1.3542 and 0.7385 
D) 1.4542 and 0.8385 
E) 1.5042 and 0.8885 
A) 1.4042 and 0.7885 
B) 1.5542 and 0.9385 
C) 1.3542 and 0.7385 
D) 1.4542 and 0.8385 
E) 1.5042 and 0.8885

Question 12

Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of $a = 10 ^ { \circ }$ in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement,calculate the coordinates $( x , y )$ of the point of intersection and use these measurements to approximate the six trigonometric functions of a $\text { "a" }$ angle.(Round your answer to two decimal places. )?   ?

Accepted Answer

A) sin10° ? 0.98,cos10° ? 0.17,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 1.02,cot10° ? 5.67 
B) sin10° ? 5.67,cos10° ? 1.02,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 0.98,cot10° ? 5.67
? 
C) sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 1.02,cot10° ? 5.67
? 
D) sin10° ? 0.18,cos10° ? 0.98,tan10° ? 0.17, csc10° ? 10,sec10° ? 0.98,cot10° ? 5.76
? 
E) sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 5.67,cot10° ? 1.02 
A) sin10° ? 0.98,cos10° ? 0.17,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 1.02,cot10° ? 5.67 
B) sin10° ? 5.67,cos10° ? 1.02,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 0.98,cot10° ? 5.67
? 
C) sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 1.02,cot10° ? 5.67
? 
D) sin10° ? 0.18,cos10° ? 0.98,tan10° ? 0.17, csc10° ? 10,sec10° ? 0.98,cot10° ? 5.76
? 
E) sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 5.67,cot10° ? 1.02

Question 13

Given sin 30° = $\frac { 1 } { 2 }$ and cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ,determine the following: ?cot 30°

Accepted Answer

A) ?cot 30° = $\frac { \sqrt { 2 } } { 2 }$ 
B) undefined 
C) ?cot 30° = $\frac { \sqrt { 3 } } { 3 }$ 
D) ?cot 30° = $\sqrt { 3 }$ 
E) ?cot 30° = 2 
A) ?cot 30° = $\frac { \sqrt { 2 } } { 2 }$ 
B) undefined 
C) ?cot 30° = $\frac { \sqrt { 3 } } { 3 }$ 
D) ?cot 30° = $\sqrt { 3 }$ 
E) ?cot 30° = 2

Question 14

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { csc } & & \frac { \pi } { 6 } & \
& & & \
\hline
\end{array}$$

Accepted Answer

A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & 2 \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 90 ^ { \circ } & \frac { \pi } { 6 } & 1 \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 45 ^ { \circ } & \frac { \pi } { 6 } & \sqrt { 2 } \
\hline
\end{array}$$ ? 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { csc } & 0 ^ { \circ } & \frac { \pi } { 6 } & 0 \
\hline
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$ 
A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & 2 \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 90 ^ { \circ } & \frac { \pi } { 6 } & 1 \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 45 ^ { \circ } & \frac { \pi } { 6 } & \sqrt { 2 } \
\hline
\end{array}$$ ? 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { csc } & 0 ^ { \circ } & \frac { \pi } { 6 } & 0 \
\hline
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Question 15

Construct an appropriate triangle to complete the table. $$\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$$ $$\begin{array} { | c | c | l | l | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 ^ { \circ } & & \
\hline
\end{array}$$

Accepted Answer

A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & 0 & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$
?
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$ 
A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & 0 & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$
?
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$

Question 16

If $\sin \theta = \frac { \sqrt { 2 } } { 2 }$ ,find the value of ? in degrees $\left( 0 ^ { \circ } < \theta < 90 ^ { \circ } \right)$ without the aid of a calculator.

Accepted Answer

A) ? = 30° 
B) ?? = 45° 
C) ??? = 90° 
D) ??? = 75° 
E) ??? = 15° 
A) ? = 30° 
B) ?? = 45° 
C) ??? = 90° 
D) ??? = 75° 
E) ??? = 15°

Question 17

Using the figure below,if ? = 26° and y = 6,determine the exact value of x.

Accepted Answer

A) ? $x = \frac { 6 } { \cot 26 ^ { \circ } }$ 
B) ? $x = \frac { 26 } { \csc 6 ^ { \circ } }$ 
C)  $x = \frac { 6 } { \tan 26 ^ { \circ } }$ 
D) ? $x = \frac { 3 } { \sin 13 ^ { \circ } }$ 
E) ? $x = \frac { 13 } { \tan 3 ^ { \circ } }$ 
A) ? $x = \frac { 6 } { \cot 26 ^ { \circ } }$ 
B) ? $x = \frac { 26 } { \csc 6 ^ { \circ } }$ 
C)  $x = \frac { 6 } { \tan 26 ^ { \circ } }$ 
D) ? $x = \frac { 3 } { \sin 13 ^ { \circ } }$ 
E) ? $x = \frac { 13 } { \tan 3 ^ { \circ } }$

Question 18

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?? $\cot \alpha = 3$ ? $\tan \alpha \text { and } \cot \left( 90 ^ { \circ } - \alpha \right)$ ?

Accepted Answer

A) ? $\tan \alpha = - \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = - \frac { 1 } { 3 }$ 
B) ? $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$ 
C)  $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$ 
D) ? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$ 
E) ? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$ 
A) ? $\tan \alpha = - \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = - \frac { 1 } { 3 }$ 
B) ? $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$ 
C)  $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$ 
D) ? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$ 
E) ? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$

Question 19

Use a calculator to evaluate tan 49°34´.Round your answer to four decimal places.

Accepted Answer

A) -1.3283 
B) 0.0423 
C) -0.8403 
D) 1.1643 
E) 1.1736 
A) -1.3283 
B) 0.0423 
C) -0.8403 
D) 1.1643 
E) 1.1736

Question 20

Evaluate each function.Round your answers to four decimal places. ?
Csc3 and $\tan \frac { 1 } { 5 }$ ?

Accepted Answer

A) 7.0862 and 0.2027 
B) 7.1862 and 0.3027 
C) 7.2362 and 0.3527 
D) 7.1362 and 0.2527 
E) 7.2862 and 0.4027 
A) 7.0862 and 0.2027 
B) 7.1862 and 0.3027 
C) 7.2362 and 0.3527 
D) 7.1362 and 0.2527 
E) 7.2862 and 0.4027

Exam 25: Right Triangle Trigonometry

Use a calculator to evaluate csc⁡(π10)\csc \left( \frac { \pi } { 10 } \right)csc(10π​) .Round your answer to four decimal places.

Evaluate each function.Round your answers to four decimal places. ​ Cos17°36' and sin67°23' ​

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. )

Evaluate each function.Round your answers to four decimal places.? sec⁡(π2−2)\sec \left( \frac { \pi } { 2 } - 2 \right)sec(2π​−2) and cot⁡(π2−13)\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)cot(2π​−31​) ?

Evaluate each function.Round your answers to four decimal places. ​ Sin22.3° and csc22.3° ​

Complete the table. \theta 0.8 0.9 1 1.1 1.2 \theta (Round your answer to four decimal places. )

Find the values of ? in degrees (0∘≤θ≤90∘)\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)(0∘≤θ≤90∘) and radians (0<θ<π2)\left( 0 < \theta < \frac { \pi } { 2 } \right)(0<θ<2π​) without the aid of a calculator. ?sin ? = 1 and csc ? = 1 ? ?

Evaluate each function.Round your answers to four decimal places. ​ Sec48°38' and csc31°57' ​

Using trigonometric identities,determine which of the following is equivalent to the following expression. ? Tan ? + cot ? ?

Find the values of ? in degrees (0∘≤θ≤90∘)\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)(0∘≤θ≤90∘) and radians (0<θ<π2)\left( 0 < \theta < \frac { \pi } { 2 } \right)(0<θ<2π​) without the aid of a calculator. sec ? = 2\sqrt { 2 }2​ and cot ? = 1 ? ?

Evaluate each function.Round your answers to four decimal places. ​ Sec0.74 and cos0.74 ​

Given sin 30° = 12\frac { 1 } { 2 }21​ and cos 30° = 32\frac { \sqrt { 3 } } { 2 }23​​ ,determine the following: ?cot 30°

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​) Function \theta() \theta() Function Value

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​) Function \theta() \theta() Function Value 3

If sin⁡θ=22\sin \theta = \frac { \sqrt { 2 } } { 2 }sinθ=22​​ ,find the value of ? in degrees (0∘<θ<90∘)\left( 0 ^ { \circ } < \theta < 90 ^ { \circ } \right)(0∘<θ<90∘) without the aid of a calculator.

Using the figure below,if ? = 26° and y = 6,determine the exact value of x.

Use a calculator to evaluate tan 49°34´.Round your answer to four decimal places.

Evaluate each function.Round your answers to four decimal places. ? Csc3 and tan⁡15\tan \frac { 1 } { 5 }tan51​ ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Use a calculator to evaluate $\csc \left( \frac { \pi } { 10 } \right)$ .Round your answer to four decimal places.

Evaluate each function.Round your answers to four decimal places. Cos17°36' and sin67°23'

Evaluate each function.Round your answers to four decimal places.? $\sec \left( \frac { \pi } { 2 } - 2 \right)$ and $\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)$ ?

Evaluate each function.Round your answers to four decimal places. Sin22.3° and csc22.3°

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. ?sin ? = 1 and csc ? = 1 ? ?

Evaluate each function.Round your answers to four decimal places. Sec48°38' and csc31°57'

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. sec ? = $\sqrt { 2 }$ and cot ? = 1 ? ?

Evaluate each function.Round your answers to four decimal places. Sec0.74 and cos0.74

Given sin 30° = $\frac { 1 } { 2 }$ and cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ,determine the following: ?cot 30°

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ Function \theta() \theta() Function Value

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ Function \theta() \theta() Function Value 3

If $\sin \theta = \frac { \sqrt { 2 } } { 2 }$ ,find the value of ? in degrees $\left( 0 ^ { \circ } < \theta < 90 ^ { \circ } \right)$ without the aid of a calculator.

Evaluate each function.Round your answers to four decimal places. ? Csc3 and $\tan \frac { 1 } { 5 }$ ?