Question 1

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-tan 41°

Accepted Answer

A) cot 49° 
B) cot 139° 
C) tan 131° 
D) cot 41° 
A) cot 49° 
B) cot 139° 
C) tan 131° 
D) cot 41°

Question 2

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-sin (-34°20´)

Accepted Answer

A) -0.5640066 
B) -0.5562956 
C) -0.5543603 
D) -0.5620834 
A) -0.5640066 
B) -0.5562956 
C) -0.5543603 
D) -0.5620834

Question 3

Solve the right triangle.
-A = 72° 6´, c = 278 m , C = 90° Round side lengths to two decimal places, if necessary.

Accepted Answer

A) B = 17° 54´, a = 264.54 m, b = 85.45 m 
B) B = 17° 6´, a = 265.74 m, b = 78.45 m 
C) B = 17° 54´, a = 264.74 m, b = 92.45 m 
D) B = 18° 44´, a = 264.74 m, b = 85.45 m 
A) B = 17° 54´, a = 264.54 m, b = 85.45 m 
B) B = 17° 6´, a = 265.74 m, b = 78.45 m 
C) B = 17° 54´, a = 264.74 m, b = 92.45 m 
D) B = 18° 44´, a = 264.74 m, b = 85.45 m

Question 4

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-2 sin 44° 14' cos 44° 14' - sin 88° 28'

Accepted Answer

A) 1 
B) 0 
C) 2 
D) -1 
A) 1 
B) 0 
C) 2 
D) -1

Question 5

Solve the problem.
-In one area, the lowest angle of elevation of the sun in winter is 21° 7´. A fence is to be built 12.4 ft away from a plant in the direction of the sun. (See drawing)Find the maximum height, x , for the
Fence so that the plant will get full sun. Round your answer to the tenths place when necessary.

Accepted Answer

A)  $6.3 \mathrm{ft}$ 
B)  $4.1 \mathrm{ft}$ 
C)  $4.8 \mathrm{ft}$ 
D)  $5.1 \mathrm{ft}$ 
A)  $6.3 \mathrm{ft}$ 
B)  $4.1 \mathrm{ft}$ 
C)  $4.8 \mathrm{ft}$ 
D)  $5.1 \mathrm{ft}$

Question 6

Find all values of , if is in the interval [0, 360°) and has the given function value.
-$$\cos \theta = \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $30 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
A)  $30 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$

Question 7

Solve the problem.
-On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and the tree is 32 meters tall, how long is the shadow?

Accepted Answer

A) 51 m 
B) 72 m 
C) 64 m 
D) 24 m 
A) 51 m 
B) 72 m 
C) 64 m 
D) 24 m

Question 8

Solve the problem.
-When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 51°11'. If Joey is known to be standing 32 feet from the base of the tree, how tall is the tree
(to the nearest foot)?

Accepted Answer

A) 40 ft 
B) 46 ft 
C) 44 ft 
D) 42 ft 
A) 40 ft 
B) 46 ft 
C) 44 ft 
D) 42 ft

Question 9

Use a calculator to decide whether the statement is true or false.
-sin (2 ·30°)= 2 · sin 30°

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 235 miles and BC is 625 miles, and if angle C is 90°, find the measure of angle B. Round your answer to
The tenths place.

Accepted Answer

A) 34.1° 
B) 20.6° 
C) 18.7° 
D) 31.4° 
A) 34.1° 
B) 20.6° 
C) 18.7° 
D) 31.4°

Question 11

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-csc 30°5´

Accepted Answer

A) 1.9939764 
B) 1.9959764 
C) 1.9949764 
D) 1.9969764 
A) 1.9939764 
B) 1.9959764 
C) 1.9949764 
D) 1.9969764

Question 12

Solve the problem.
-Snell's Law states that $\frac { c _ { 1 } } { c _ { 2 } } = \frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } }$. Use this law to find the requested value. If $c _ { 1 } = 7 \times 10 ^ { 7 }$, $\theta _ { 1 } = 48 ^ { \circ }$, and $\theta _ { 2 } = 33 ^ { \circ }$, find $c _ { 2 }$.

Accepted Answer

A)  $\mathrm { c } _ { 2 } = 4.89 \times 10 ^ { 9 }$ 
B)  $c _ { 2 } = 5.13 \times 10 ^ { 6 }$ 
C)  $c _ { 2 } = 5.66 \times 10 ^ { 7 }$ 
D)  $\mathrm { c } _ { 2 } = 5.13 \times 10 ^ { 7 }$ 
A)  $\mathrm { c } _ { 2 } = 4.89 \times 10 ^ { 9 }$ 
B)  $c _ { 2 } = 5.13 \times 10 ^ { 6 }$ 
C)  $c _ { 2 } = 5.66 \times 10 ^ { 7 }$ 
D)  $\mathrm { c } _ { 2 } = 5.13 \times 10 ^ { 7 }$

Question 13

Find the sign of the following.
-sec (-ϴ), given that ϴ is in the interval (180°, 270°).

Accepted Answer

A) positive 
B) negative 
A) positive 
B) negative

Question 14

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-sec 29.7°

Accepted Answer

A) cos 60.3° 
B) cos 150.3° 
C) csc 60.3° 
D) csc 29.7° 
A) cos 60.3° 
B) cos 150.3° 
C) csc 60.3° 
D) csc 29.7°

Question 15

Solve the problem.
-A formula used by an engineer to determine the safe radius of a curve, $R$, when designing a road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$, where $\alpha$ is the superelevation of the road and $\mathrm { V }$ is the velocity (in feet per second) for which the curve is designed. If $\mathrm { V } = 84 \mathrm { ft }$ per $\mathrm { sec } , \mathrm { f } = 0.1 , \mathrm {~g} = 30$, and $\alpha = 1.1 ^ { \circ }$, find $\mathrm { R }$. Round to the nearest foot.

Accepted Answer

A)  $\mathrm { R } = 1973 \mathrm { ft }$ 
B)  $R = 1977 \mathrm { ft }$ 
C)  $R = 1983 \mathrm { ft }$ 
D)  $\mathrm { R } = 1970 \mathrm { ft }$ 
A)  $\mathrm { R } = 1973 \mathrm { ft }$ 
B)  $R = 1977 \mathrm { ft }$ 
C)  $R = 1983 \mathrm { ft }$ 
D)  $\mathrm { R } = 1970 \mathrm { ft }$

Question 16

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an
airplane located at that point. Express the bearing using both methods.
-( , 0)

Accepted Answer

A) 270°; N 90° E or S 90° E 
B) 90°; N 90° W or S 90° W 
C) 270°; N 90° W or S 90° W 
D) 90°; N 90° E or S 90° E 
A) 270°; N 90° E or S 90° E 
B) 90°; N 90° W or S 90° W 
C) 270°; N 90° W or S 90° W 
D) 90°; N 90° E or S 90° E

Question 17

Evaluate.
-$2 \cot ^ { 2 } 270 ^ { \circ } + 2 \sec ^ { 2 } 0 ^ { \circ } - \csc ^ { 2 } 225 ^ { \circ }$

Accepted Answer

A)  0 
B)  $\frac { 3 } { 2 }$ 
C)  4 
D)  $\frac { 5 } { 2 }$ 
A)  0 
B)  $\frac { 3 } { 2 }$ 
C)  4 
D)  $\frac { 5 } { 2 }$

Question 18

Use a calculator to decide whether the statement is true or false.
-sin (180°+ 225°)= sin 180° · cos 225° + cos 180° · sin 225°

Accepted Answer

A) True 
 B)False

Question 19

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-Radio direction finders are set up at points A and B, 8.68 mi apart on an east-west line. From A it is found that the bearing of a signal from a transmitter is N 54.3°E, while from B it is N 35.7°W. Find
The distance of the transmitter from B, to the nearest hundredth of a mile.

Accepted Answer

A) 4.57 mi 
B) 7.05 mi 
C) 5.07 mi 
D) 7.55 mi 
A) 4.57 mi 
B) 7.05 mi 
C) 5.07 mi 
D) 7.55 mi

Question 20

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$B = 53 ^ { \circ } 47 ^ { \prime } , b = 25 \mathrm {~km}$
Round side lengths to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 42.3 \mathrm {~km} ; \mathrm { a } = 18.3 \mathrm {~km}$ 
B)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 31.0 \mathrm {~km} ; \mathrm { a } = 18.3 \mathrm {~km}$ 
C)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 42.3 \mathrm {~km} ; \mathrm { a } = 31.0 \mathrm {~km}$ 
D)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 31.1 \mathrm {~km} ; \mathrm { a } = 42.0 \mathrm {~km}$ 
A)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 42.3 \mathrm {~km} ; \mathrm { a } = 18.3 \mathrm {~km}$ 
B)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 31.0 \mathrm {~km} ; \mathrm { a } = 18.3 \mathrm {~km}$ 
C)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 42.3 \mathrm {~km} ; \mathrm { a } = 31.0 \mathrm {~km}$ 
D)  $\mathrm { A } = 36 ^ { \circ } 13 ^ { \prime } ; \mathrm { c } = 31.1 \mathrm {~km} ; \mathrm { a } = 42.0 \mathrm {~km}$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -tan 41°

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -sin (-34°20´)

Solve the right triangle. -A = 72° 6´, c = 278 m , C = 90° Round side lengths to two decimal places, if necessary.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -2 sin 44° 14' cos 44° 14' - sin 88° 28'

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\cos \theta = \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and the tree is 32 meters tall, how long is the shadow?

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 51°11'. If Joey is known to be standing 32 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Use a calculator to decide whether the statement is true or false. -sin (2 ·30°)= 2 · sin 30°

Solve the problem. -A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 235 miles and BC is 625 miles, and if angle C is 90°, find the measure of angle B. Round your answer to The tenths place.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -csc 30°5´

Find the sign of the following. -sec (-ϴ), given that ϴ is in the interval (180°, 270°).

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -sec 29.7°

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. -( , 0)

Evaluate. - $2 \cot ^ { 2 } 270 ^ { \circ } + 2 \sec ^ { 2 } 0 ^ { \circ } - \csc ^ { 2 } 225 ^ { \circ }$

Use a calculator to decide whether the statement is true or false. -sin (180°+ 225°)= sin 180° · cos 225° + cos 180° · sin 225°

Trigonometric Functions

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 2: Acute Angles and Right Triangles