Question 1

Use a calculator to evaluate tan 68°23'.Round your answer to four decimal places.

Accepted Answer

A) 2.5236 
B) 2.5040 
C) -1.2222 
D) -0.8980 
E) 0.7269 
A) 2.5236 
B) 2.5040 
C) -1.2222 
D) -0.8980 
E) 0.7269 A

Question 2

A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly.From point A the biologist walks downstream $x = 140$ feet and sights to point C (see figure).From this sighting,it is determined that ? = 54°.How wide is the river??   (Round your answer to three decimal places. ) ?

Accepted Answer

A) 212.693 
B) 197.693 
C) 207.693 
D) 202.693 
E) 192.693 
A) 212.693 
B) 197.693 
C) 207.693 
D) 202.693 
E) 192.693 E

Question 3

A tapered shaft has a diameter of $x = 9$ centimeters at the small end and is 15 centimeters long (see figure).The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. )?   ? ?

Accepted Answer

A) 10.57 cm 
B) 14.57 cm 
C) 12.57 cm 
D) 18.57 cm 
E) 16.57 cm 
A) 10.57 cm 
B) 14.57 cm 
C) 12.57 cm 
D) 18.57 cm 
E) 16.57 cm A

Question 4

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower $x = 100$ feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire. ??   ?

Accepted Answer

A) 166.6 ft 
B) ?146.6 ft 
C) ?156.6 ft 
D) ?161.6 ft 
E) ?151.6 ft 
A) 166.6 ft 
B) ?146.6 ft 
C) ?156.6 ft 
D) ?161.6 ft 
E) ?151.6 ft

Question 5

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive $x = 23$ miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place. )?   ?

Accepted Answer

A) 10.3 mi 
B) 2.3 mi 
C) 4.3 mi 
D) 8.3 mi 
E) 6.3 mi 
A) 10.3 mi 
B) 2.3 mi 
C) 4.3 mi 
D) 8.3 mi 
E) 6.3 mi

Question 6

Find the exact value of csc ?,using the triangle shown in the figure below,if a = 3 and b = 4.

Accepted Answer

A)  $$\frac { 5 } { 4 }$$ 
B) ? $\frac { 5 } { 3 }$ 
C) ? $\frac { 3 } { 4 }$ 
D) ? $$\frac { 4 } { 5 }$$ 
E) ? $\frac { 3 } { 5 }$ 
A)  $$\frac { 5 } { 4 }$$ 
B) ? $\frac { 5 } { 3 }$ 
C) ? $\frac { 3 } { 4 }$ 
D) ? $$\frac { 4 } { 5 }$$ 
E) ? $\frac { 3 } { 5 }$

Question 7

You are skiing down a mountain with a vertical height of 1250 feet.The distance from the top of the mountain to the base is 2500 feet.What is the angle of elevation from the base to the top of the mountain? ?

Accepted Answer

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

Question 8

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. cos ? = 0 and tan ? = Not defined
?
?

Accepted Answer

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

Question 9

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. ) ​

Accepted Answer

A) 45 m 
B) 41 m 
C) 43 m 
D) 49 m 
E) 47 m 
A) 45 m 
B) 41 m 
C) 43 m 
D) 49 m 
E) 47 m

Question 10

Find the exact values of the six trigonometric functions of the angle ? for each of the two triangles.     ?

Accepted Answer

A) sin ? = $$\frac { 15 } { 8 }$$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 8 } { 15 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 15 } { 17 }$
? 
B) sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
? 
C) sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
? 
D) sin ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
? 
E) sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
? 
A) sin ? = $$\frac { 15 } { 8 }$$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 8 } { 15 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 15 } { 17 }$
? 
B) sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
? 
C) sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
? 
D) sin ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
? 
E) sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
?

Question 11

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 $$\begin{array} { | c | c | l | l | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 ^ { \circ } & & \
\hline
\end{array}$$

Accepted Answer

A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \\
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \\
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & 0 & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 2 } & 1
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$ 
A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \\
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \\
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & 0 & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 2 } & 1
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$

Question 12

If ? is an acute angle and $\cot \theta = \frac { 1 } { 4 }$ ,determine sin ?.

Accepted Answer

A)  $\sin \theta = \frac { \sqrt { 17 } } { 4 }$ 
B) ? $\sin \theta = \sqrt { 17 }$ 
C) ? $\sin \theta = 4$ 
D) ? $\sin \theta = \frac { \sqrt { 17 } } { 17 }$ 
E) ? $\sin \theta = \frac { 4 \sqrt { 17 } } { 17 }$ 
A)  $\sin \theta = \frac { \sqrt { 17 } } { 4 }$ 
B) ? $\sin \theta = \sqrt { 17 }$ 
C) ? $\sin \theta = 4$ 
D) ? $\sin \theta = \frac { \sqrt { 17 } } { 17 }$ 
E) ? $\sin \theta = \frac { 4 \sqrt { 17 } } { 17 }$

Question 13

Select a right triangle corresponding to the trigonometric function of the acute angle ?.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of ?. ?
Tan ? = $\frac { 5 } { 12 }$ ?
?
Sin ? = $\frac { 5 } { 13 }$ csc ? = $\frac { 13 } { 5 }$ cos ? = $\frac { 12 } { 13 }$ sec ? = $\frac { 13 } { 12 }$ tan ? = $\frac { 5 } { 12 }$ cot ? = $\frac { 12 } { 5 }$ ?

Accepted Answer

A) ?   sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 13 } { 12 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 5 }$
? 
B) ?   sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 12 } { 5 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 13 } { 12 }$
? 
C) ?   sin ? = $$\frac { 13 } { 12 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 5 }$
Sec ? = $\frac { 5 } { 13 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 13 }$
? 
D) ?   sin ? = $$\frac { 13 } { 5 }$$
Csc ? = $\frac { 5 } { 13 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 12 } { 5 }$
Cot ? = $\frac { 5 } { 12 }$
? 
E) ?   sin ? = $$\frac { 12 } { 5 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 5 } { 13 }$
? 
A) ?   sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 13 } { 12 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 5 }$
? 
B) ?   sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 12 } { 5 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 13 } { 12 }$
? 
C) ?   sin ? = $$\frac { 13 } { 12 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 5 }$
Sec ? = $\frac { 5 } { 13 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 13 }$
? 
D) ?   sin ? = $$\frac { 13 } { 5 }$$
Csc ? = $\frac { 5 } { 13 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 12 } { 5 }$
Cot ? = $\frac { 5 } { 12 }$
? 
E) ?   sin ? = $$\frac { 12 } { 5 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 5 } { 13 }$
?

Question 14

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 ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
? 
B) sin ? = $\frac { 17 } { 8 }$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 15 } { 8 }$
Cot ? = $\frac { 8 } { 15 }$
? 
C) sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
? 
D) sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
? 
E) sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
? 
A) sin ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
? 
B) sin ? = $\frac { 17 } { 8 }$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 15 } { 8 }$
Cot ? = $\frac { 8 } { 15 }$
? 
C) sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
? 
D) sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
? 
E) sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
?

Question 15

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

Accepted Answer

A) ?sec 30° = 1 
B) ?sec 30° = $\sqrt { 3 }$ 
C) ?sec 30° = $\frac { 2 \sqrt { 3 } } { 3 }$ 
D) ?sec 30° = $\frac { \sqrt { 2 } } { 2 }$ 
E) undefined 
A) ?sec 30° = 1 
B) ?sec 30° = $\sqrt { 3 }$ 
C) ?sec 30° = $\frac { 2 \sqrt { 3 } } { 3 }$ 
D) ?sec 30° = $\frac { \sqrt { 2 } } { 2 }$ 
E) undefined

Question 16

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

Accepted Answer

A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 30 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { cot } & 90 ^ { \circ } & \frac { \pi } { 2 } & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 0 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \
\hline
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \\cot & 60 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \\
\hline
\end{array}$$ 
A) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 30 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \
\hline
\end{array}$$ 
B) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$ 
C) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { cot } & 90 ^ { \circ } & \frac { \pi } { 2 } & 0 \
\hline
\end{array}$$ 
D) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 0 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \
\hline
\end{array}$$ 
E) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \\cot & 60 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \\
\hline
\end{array}$$

Question 17

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

Accepted Answer

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

Question 18

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & & \frac { \pi } { 3 } & \
\hline
\end{array}$$

Accepted Answer

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) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 30 ^ { \circ } & \frac { \pi } { 3 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$ 
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 19

A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures $\theta$ .(Round your answers to one decimal places. ) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & & & & & \
\hline
\end{array}$$

Accepted Answer

A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 5.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle } , \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 7.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 4.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 3.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 6.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 5.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle } , \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 7.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 4.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 3.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 6.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$

Question 20

Use a graphing utility to complete the table. $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & & & & & \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & & & & & \
\hline
\end{array}$$

Accepted Answer

A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$ 
A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$

Exam 25: Right Triangle Trigonometry

Use a calculator to evaluate tan 68°23'.Round your answer to four decimal places.

A tapered shaft has a diameter of x=9x = 9x=9 centimeters at the small end and is 15 centimeters long (see figure).The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. )? ? ?

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower x=100x = 100x=100 feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire. ?? ?

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive x=23x = 23x=23 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place. )? ?

Find the exact value of csc ?,using the triangle shown in the figure below,if a = 3 and b = 4.

You are skiing down a mountain with a vertical height of 1250 feet.The distance from the top of the mountain to the base is 2500 feet.What is the angle of elevation from the base to the top of the mountain? ?

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. cos ? = 0 and tan ? = Not defined ? ?

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. ) ​

Find the exact values of the six trigonometric functions of the angle ? for each of the two triangles. ?

If ? is an acute angle and cot⁡θ=14\cot \theta = \frac { 1 } { 4 }cotθ=41​ ,determine sin ?.

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. ) ?

Given sin⁡30∘=12\sin 30 ^ { \circ } = \frac { 1 } { 2 }sin30∘=21​ and cos⁡30∘=32\cos 30 ^ { \circ } = \frac { \sqrt { 3 } } { 2 }cos30∘=23​​ ,determine the following: ?sec 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 ?

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

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( rad ) Function Value

A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures θ\thetaθ .(Round your answers to one decimal places. ) Angle, \theta 5 4 3 2 1 Height

Use a graphing utility to complete the table. \theta 2 3 4 5 6 \theta 9-\theta

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

Rotation of Conics

A tapered shaft has a diameter of $x = 9$ centimeters at the small end and is 15 centimeters long (see figure).The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. )? ? ?

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower $x = 100$ feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire. ?? ?

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive $x = 23$ miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place. )? ?

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. cos ? = 0 and tan ? = Not defined ? ?

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. )

If ? is an acute angle and $\cot \theta = \frac { 1 } { 4 }$ ,determine sin ?.

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

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

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( rad ) Function Value

A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures $\theta$ .(Round your answers to one decimal places. ) Angle, \theta 5 4 3 2 1 Height