Question 1

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 5 cos 2x

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is $3.0 \times 10 ^ { 8 }$ . What is the frequency of the radar waves?

Accepted Answer

A)  7.1 $\times 10 ^ { 6 }$ Hz 
B)  7.1 $\times 10 ^ { 9 }$ Hz 
C)  6.7 $\times 10 ^ { 9 }$ MHz 
D)  7.1 $\times 10 ^ { 9 }$ MHz 
E)  6.7 $\times 10 ^ { 9 }$ Hz 
A)  7.1 $\times 10 ^ { 6 }$ Hz 
B)  7.1 $\times 10 ^ { 9 }$ Hz 
C)  6.7 $\times 10 ^ { 9 }$ MHz 
D)  7.1 $\times 10 ^ { 9 }$ MHz 
E)  6.7 $\times 10 ^ { 9 }$ Hz

Question 3

Find the value of tan 125.1° rounded to four significant digits.

Accepted Answer

A)  -1.223 
B)  1.423 
C)  -0.711 
D)  -1.423 
E)  0.711 
A)  -1.223 
B)  1.423 
C)  -0.711 
D)  -1.423 
E)  0.711

Question 4

Find the value of sin 301.8° rounded to four significant digits.

Accepted Answer

A)  -1.1199 
B)  -0.4449 
C)  -1.1749 
D)  0 
E)  -0.8499 
A)  -1.1199 
B)  -0.4449 
C)  -1.1749 
D)  0 
E)  -0.8499

Question 5

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation.   $y = 15 \sin \left( \frac { 2 } { 3 } x - 210 ^ { \circ } \right)$

Accepted Answer

A)  P = 540°, A = 15, S = -315°   
B)  P = 24°, A = 0.67, S = -14°   
C)  P = 24°, A = 0.67, S = -14°   
D)  P = 540°, A = 15, S = 315°   
E)  P = 540°, A = 15, S = -315°   
A)  P = 540°, A = 15, S = -315°   
B)  P = 24°, A = 0.67, S = -14°   
C)  P = 24°, A = 0.67, S = -14°   
D)  P = 540°, A = 15, S = 315°   
E)  P = 540°, A = 15, S = -315°

Question 6

A contractor needs to grade the slope of a subdivision lot to place a house on level ground. (See the illustration.) The present slope of the lot is 10.5°. The contractor needs a level lot that is 106 ft deep. To control erosion, the back of the lot must be cut to a slope of 23.2°. How far from the street, measured along the present slope, will the excavation extend? Round your answer to the nearest foot.

Accepted Answer

A)  184 ft 
B)  190 ft 
C)  196 ft 
D)  168 ft 
E)  210 ft 
A)  184 ft 
B)  190 ft 
C)  196 ft 
D)  168 ft 
E)  210 ft

Question 7

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 55.0°, b = 4,120 ft, c = 4,540 ft

Accepted Answer

A)  C = 60.5°, A = 64.5°, a = 2,610 ft 
B)  C = 64.5°, A = 9.5°, a = 2,610 ft 
C)  C = 115.5°, A = 9.5°, a = 831 ft 
D)  C = 64.5°, A = 60.5°, a = 4,380 ft 
E)  No solution. 
A)  C = 60.5°, A = 64.5°, a = 2,610 ft 
B)  C = 64.5°, A = 9.5°, a = 2,610 ft 
C)  C = 115.5°, A = 9.5°, a = 831 ft 
D)  C = 64.5°, A = 60.5°, a = 4,380 ft 
E)  No solution.

Question 8

Find the period P and amplitude A and graph at least two periods of the equation. $y = 3 \sin \frac { 1 } { 3 } x$

Accepted Answer

A)  P = 1080°, A = 3   
B)  P = 1080°, A = 3   
C)  P = 120°, A = 0.33   
D)  P = 1080°, A = 3   
E)  P = 120°, A = 0.33   
A)  P = 1080°, A = 3   
B)  P = 1080°, A = 3   
C)  P = 120°, A = 0.33   
D)  P = 1080°, A = 3   
E)  P = 120°, A = 0.33

Question 9

Find the value of tan 174.6° rounded to four significant digits.

Accepted Answer

A)  0.2055 
B)  0.0945 
C)  -0.0473 
D)  -0.0945 
E)  0.0473 
A)  0.2055 
B)  0.0945 
C)  -0.0473 
D)  -0.0945 
E)  0.0473

Question 10

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). C = 73.5°, a = 244 cm, c = 234 cm

Accepted Answer

A)  A = 91.2°, B = 15.3°, b = 64.6 cm 
B)  A = 91.2°, B = 15.3°, b = 77 cm 
C)  A = 15.3°, B = 88.8°, b = 77 cm 
D)  A = 88.8°, B = 17.7°, b = 74 cm 
E)  No solution. 
A)  A = 91.2°, B = 15.3°, b = 64.6 cm 
B)  A = 91.2°, B = 15.3°, b = 77 cm 
C)  A = 15.3°, B = 88.8°, b = 77 cm 
D)  A = 88.8°, B = 17.7°, b = 74 cm 
E)  No solution.

Question 11

Find the period P and amplitude A and graph at least two periods of the equation. y = 4 sin 2x

Accepted Answer

A)  P = 90° , A = 2   
B)   P = 180° , A = 4   
C)  P = 180° , A = 4   
D)  P = 90° , A = 2   
E)  P = 180°, A = 4   
A)  P = 90° , A = 2   
B)   P = 180° , A = 4   
C)  P = 180° , A = 4   
D)  P = 90° , A = 2   
E)  P = 180°, A = 4

Question 12

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). $$\angle B = 62.9$$ °, b = 135 m, c = 118 m

Accepted Answer

A)  a = 118 m, $\angle A = 37.7$ °, $\angle C = 79.4$ ° 
B)  a = 139 m, $\angle A = 37.7$ °, $\angle C = 51.1$ ° 
C)  a = 139 m, $\angle A = 66.0$ °, $\angle C = 51.1$ ° 
D)  a = 118 m, $\angle A = 66.0$ °, $\angle C = 51.1$ ° 
E)  a = 139 m, $\angle A = 37.7$ °, $\angle C = 79.4$ ° 
A)  a = 118 m, $\angle A = 37.7$ °, $\angle C = 79.4$ ° 
B)  a = 139 m, $\angle A = 37.7$ °, $\angle C = 51.1$ ° 
C)  a = 139 m, $\angle A = 66.0$ °, $\angle C = 51.1$ ° 
D)  a = 118 m, $\angle A = 66.0$ °, $\angle C = 51.1$ ° 
E)  a = 139 m, $\angle A = 37.7$ °, $\angle C = 79.4$ °

Question 13

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 41.9°, b = 143 cm, c = 281 cm

Accepted Answer

A)  C = 43.0°, A = 95.1°, a = 120 cm 
B)  C = 43.0°, A = 95.1°, a = 124 cm 
C)  C = 43.0°, A = 95.1°, a = 116 cm 
D)  C = 95.1°, A = 43.0°, a = 120 cm 
E)  No solution. 
A)  C = 43.0°, A = 95.1°, a = 120 cm 
B)  C = 43.0°, A = 95.1°, a = 124 cm 
C)  C = 43.0°, A = 95.1°, a = 116 cm 
D)  C = 95.1°, A = 43.0°, a = 120 cm 
E)  No solution.

Question 14

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). $\angle C = 48.2$ °, $\angle B = 54.9$ °, b = 5,910 m

Accepted Answer

A)  a = 7,040 m, c = 5,390 m, $\angle A = 76.9$ ° 
B)  a = 7,040 m, c = 5,390 m, $\angle A = 48.2$ ° 
C)  a = 5,390 m, c = 7,040 m, $\angle A = 48.2$ ° 
D)  a = 5,390 m, c = 7,040 m, $\angle A = 76.9$ ° 
E)  a = 5,910 m, c = 5,390 m, $\angle A = 76.9$ ° 
A)  a = 7,040 m, c = 5,390 m, $\angle A = 76.9$ ° 
B)  a = 7,040 m, c = 5,390 m, $\angle A = 48.2$ ° 
C)  a = 5,390 m, c = 7,040 m, $\angle A = 48.2$ ° 
D)  a = 5,390 m, c = 7,040 m, $\angle A = 76.9$ ° 
E)  a = 5,910 m, c = 5,390 m, $\angle A = 76.9$ °

Question 15

Find the lengths of rafters AC and BC of the roof shown in the Illustration.

Accepted Answer

A)  AC = 29.2 ft, BC = 19.7 ft 
B)  AC = 25.3 ft, BC = 25.4 ft 
C)  AC = 29.2 ft, BC = 19 ft 
D)  AC = 25.3 ft, BC = 19.0 ft 
E)  AC = 25.3 ft, BC = 19.7 ft 
A)  AC = 29.2 ft, BC = 19.7 ft 
B)  AC = 25.3 ft, BC = 25.4 ft 
C)  AC = 29.2 ft, BC = 19 ft 
D)  AC = 25.3 ft, BC = 19.0 ft 
E)  AC = 25.3 ft, BC = 19.7 ft

Question 16

Find the period P and amplitude A and graph at least two periods of the equation. $y = 4.8 \sin \frac { 2 } { 3 } x$

Accepted Answer

A)  P = 240.0°, A = 4.80   
B)  P = 240.0°, A = 4.80   
C)  P = 75.0°, A = 0.67   
D)  P = 540°, A = 4.80   
E)  P = 540°, A = 4.80   
A)  P = 240.0°, A = 4.80   
B)  P = 240.0°, A = 4.80   
C)  P = 75.0°, A = 0.67   
D)  P = 540°, A = 4.80   
E)  P = 540°, A = 4.80

Question 17

The average distance from the sun to earth is $1.5 \times 10 ^ { 8 }$ and from the sun to Venus is $1.1 \times 10 ^ { 8 }$ . Find the distance between earth and Venus when the angle between earth and the sun and earth and Venus is 24.9°. Do not use rounded answers during calculations. Round the final answer to two significant digits.

Accepted Answer

A)  $2.3 \times 10 ^ { 8 }$ km 
B)  $0.46 \times 10 ^ { 8 }$ km 
C)  $1.4 \times 10 ^ { 8 }$ km 
D)  $0.23 \times 10 ^ { 8 }$ km 
E)  No solution. 
A)  $2.3 \times 10 ^ { 8 }$ km 
B)  $0.46 \times 10 ^ { 8 }$ km 
C)  $1.4 \times 10 ^ { 8 }$ km 
D)  $0.23 \times 10 ^ { 8 }$ km 
E)  No solution.

Question 18

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 8.0°, b = 459 m, c = 853 m

Accepted Answer

A)  C = 165.0°, A = 7.0°, a = 401 m 
B)  C = 15.0°, A = 157.0°, a = 1,290 m 
C)  C = 165.0°, A = 157.0°, a = 846 m 
D)  C = 15.0°, A = 7.0°, a = 846 m 
E)  No solution. 
A)  C = 165.0°, A = 7.0°, a = 401 m 
B)  C = 15.0°, A = 157.0°, a = 1,290 m 
C)  C = 165.0°, A = 157.0°, a = 846 m 
D)  C = 15.0°, A = 7.0°, a = 846 m 
E)  No solution.

Question 19

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). $\angle B = 108.0$ °, c = 10.2 km, b = 31.0 km

Accepted Answer

A)  a = 10.2 km, $\angle A = 18.2$ °, $\angle C = 53.8$ ° 
B)  a = 31.0 km, $\angle A = 53.8$ °, $\angle C = 18.2$ ° 
C)  a = 26.3 km, $\angle A = 53.8$ °, $\angle C = 18.2$ ° 
D)  a = 31.0 km, $\angle A = 18.2$ °, $\angle C = 53.8$ ° 
E)  a = 26.3 km, $\angle A = 18.2$ °, $\angle C = 53.8$ ° 
A)  a = 10.2 km, $\angle A = 18.2$ °, $\angle C = 53.8$ ° 
B)  a = 31.0 km, $\angle A = 53.8$ °, $\angle C = 18.2$ ° 
C)  a = 26.3 km, $\angle A = 53.8$ °, $\angle C = 18.2$ ° 
D)  a = 31.0 km, $\angle A = 18.2$ °, $\angle C = 53.8$ ° 
E)  a = 26.3 km, $\angle A = 18.2$ °, $\angle C = 53.8$ °

Question 20

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. y = 3 cos (3x + 60°)

Accepted Answer

A)  P = 120°, A = 2, S = 20°   
B)  P = 180°, A = 3, S = -30°   
C)  P = 120°, A = 2, S = 20°   
D)  P = 180°, A = 3, S = 30°   
E)  P = 120°, A = 2, S = 20°   
A)  P = 120°, A = 2, S = 20°   
B)  P = 180°, A = 3, S = -30°   
C)  P = 120°, A = 2, S = 20°   
D)  P = 180°, A = 3, S = 30°   
E)  P = 120°, A = 2, S = 20°

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 5 cos 2x

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is $3.0 \times 10 ^ { 8 }$ . What is the frequency of the radar waves?

Find the value of tan 125.1° rounded to four significant digits.

Find the value of sin 301.8° rounded to four significant digits.

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. $y = 15 \sin \left( \frac { 2 } { 3 } x - 210 ^ { \circ } \right)$

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 55.0°, b = 4,120 ft, c = 4,540 ft

Find the period P and amplitude A and graph at least two periods of the equation. $y = 3 \sin \frac { 1 } { 3 } x$

Find the value of tan 174.6° rounded to four significant digits.

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). C = 73.5°, a = 244 cm, c = 234 cm

Find the period P and amplitude A and graph at least two periods of the equation. y = 4 sin 2x

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 41.9°, b = 143 cm, c = 281 cm

Find the lengths of rafters AC and BC of the roof shown in the Illustration.

Find the period P and amplitude A and graph at least two periods of the equation. $y = 4.8 \sin \frac { 2 } { 3 } x$

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 8.0°, b = 459 m, c = 853 m

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. y = 3 cos (3x + 60°)

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 14: Trigonometry With Any Angle

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 5 cos 2x

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is 3.0×1083.0 \times 10 ^ { 8 }3.0×108 . What is the frequency of the radar waves?

Find the value of tan 125.1° rounded to four significant digits.

Find the value of sin 301.8° rounded to four significant digits.

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. y=15sin⁡(23x−210∘)y = 15 \sin \left( \frac { 2 } { 3 } x - 210 ^ { \circ } \right)y=15sin(32​x−210∘)

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 55.0°, b = 4,120 ft, c = 4,540 ft

Find the period P and amplitude A and graph at least two periods of the equation. y=3sin⁡13xy = 3 \sin \frac { 1 } { 3 } xy=3sin31​x

Find the value of tan 174.6° rounded to four significant digits.

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). C = 73.5°, a = 244 cm, c = 234 cm

Find the period P and amplitude A and graph at least two periods of the equation. y = 4 sin 2x

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). ∠B=62.9\angle B = 62.9∠B=62.9 °, b = 135 m, c = 118 m

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 41.9°, b = 143 cm, c = 281 cm

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). ∠C=48.2\angle C = 48.2∠C=48.2 °, ∠B=54.9\angle B = 54.9∠B=54.9 °, b = 5,910 m

Find the lengths of rafters AC and BC of the roof shown in the Illustration.

Find the period P and amplitude A and graph at least two periods of the equation. y=4.8sin⁡23xy = 4.8 \sin \frac { 2 } { 3 } xy=4.8sin32​x

Solve the triangle given below. Do not round results during calculations. (For answers, round lengths to three significant digits and angles to the nearest tenth of a degree). B = 8.0°, b = 459 m, c = 853 m

Solve the triangle using the labels as shown in the illustration (round lengths of sides to three significant digits and angles to the nearest tenth of a degree). ∠B=108.0\angle B = 108.0∠B=108.0 °, c = 10.2 km, b = 31.0 km

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. y = 3 cos (3x + 60°)

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Basic Statistics

Binary and Hexadecimal Numbers

Filters

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is $3.0 \times 10 ^ { 8 }$ . What is the frequency of the radar waves?

Find the period P, amplitude A, and phase shift S, and graph at least two periods of the equation. $y = 15 \sin \left( \frac { 2 } { 3 } x - 210 ^ { \circ } \right)$

Find the period P and amplitude A and graph at least two periods of the equation. $y = 3 \sin \frac { 1 } { 3 } x$

Find the period P and amplitude A and graph at least two periods of the equation. $y = 4.8 \sin \frac { 2 } { 3 } x$