Deck 5: Trigonometric Functions

Question 1

Find the value of the trigonometric function to four decimal places. cos 35 °

A)-0.4282
B)0.5736
C)0.8192
D)-0.9037
E)1.2208

Answer 1

0.8192

Question 2

Find the number of radians in 4 revolutions. Leave answer in terms of p .

A)
B)
C)
D)
E)

Answer 2

Question 3

Angle of Rotation and Distance. The minute hand on the clock atop city hall measures 6 feet 3 inches from its tip to its axle. Through what angle (in radians)does the minute hand pass between 9:17 A.M. and 9:40 A.M.?

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the measure of the complement and the supplement of the angle, if possible. 5 ° 8 ¢

A)84 ° 92 ¢, 174 ° 92 ¢
B)Does not exist
C)85 ° 52 ¢, 175 ° 52 ¢
D)84 ° 82 ¢, 174 ° 82 ¢
E)84 ° 52 ¢, 174 ° 52 ¢

Question 5

Find the exact value of the expression. sin cos

A)
B)
C)
D)
E)

Question 6

Convert the degree measure of the angle to radians. Round answer to the nearest hundredth. 223 °

A)7.78
B)7.01
C)2.59
D)1.28
E)3.89

Question 7

Find the area of the following triangle given a = 13 in, b = 20 in, and q = 44 . Round answer to the nearest integer.

A)181 in²
B)90 in²
C)59 in²
D)94 in²
E)139 in²

Question 8

Distance Across a Marsh. In the diagram below, D ABC is a right triangle and AB represents the distance across a marsh. If C measures 37 and BC measures 44 m, find AB. Round answer to the nearest meter.

A)34 m
B)35 m
C)26 m
D)33 m
E)36 m

Question 9

Find the measure of the reference angle q ¢ given q = 1398°.

A)228 °
B)318 °
C)138 °
D)42 °
E)48 °

Question 10

Convert the DMS measure to its equivalent decimal degree measure. Round answer to three decimal places. 213 ° 29 ¢ 48 ²

A)213.483
B)212.503
C)213.497
D)213.883
E)214.283

Question 11

Angular Rotation of Two Pulleys. A pulley with a radius of 17 inches uses a belt to drive a pulley with a radius of 24 inches. The 17-inch pulley turns through an angle of 150 ° . Find the radian measure of the angle through which the 24-inch pulley turns.

A)
B)
C)
D)
E)

Question 12

Area of an Isosceles Triangle. Consider an isosceles triangle with legs measuring 21 cm each and base angles measuring 26° each. Find the area of the triangle. Round to the nearest integer.

A)85 cm²
B)105 cm²
C)356 cm²
D)87 cm²
E)174 cm²

Question 13

Convert the radian measure to exact degree measure.

A)80 °
B)502.4 °
C)160 °
D)202.5 °
E)320 °

Question 14

Linear Speed of a Truck. Each tire on a truck has a radius of 16 inches. The tires are rotating at 440 revolutions per minute. Find the speed of the truck to the nearest mile per hour.

A)13 mph
B)31 mph
C)21 mph
D)80 mph
E)42 mph

Question 15

Height of a Building. A surveyor determines that the angle of elevation from a transit to the top of a building is 26.4 . The transit is positioned 4.8 feet above ground level and 126 feet from the building. Find the height of the building to the nearest tenth of a foot.

A)67.3 ft
B)117.7 ft
C)62.5 ft
D)57.7 ft
E)60.8 ft

Question 16

Angular Rotation of Two Pulleys. A pulley with a diameter of 1.4 meters uses a belt to drive a pulley with a diameter of 0.4 meter. The 1.4-meter pulley turns through an angle of 240 ° . Find the degree measure of the angle through which the 0.4-meter pulley turns.

A)
B)
C)
D)
E)

Question 17

Find the value of the trigonometric function to four decimal places. tan 41.1°

A)1.1463
B)3.7698
C)0.8724
D)0.2653
E)1.3270

Question 18

Use the Reference Angle Theorem to find the exact value of the trigonometric function.

A)
B)
C)
D)
E)

Question 19

Distance of a Descent. An airplane traveling at 242 mph is descending at an angle of depression of 8°. How many miles will the plane descend in 8 minutes? Round answer to the nearest tenth of a mile.

A)33.7 mi
B)31.9 mi
C)32.0 mi
D)4.5 mi
E)5.6 mi

Question 20

Width of a Ramp. A skateboarder wishes to build a jump ramp that is inclined at a 11° angle and that has a maximum height of 29.2 inches. Find the horizontal width of the ramp. Round answer to the nearest tenth of an inch.

A)153.0 in
B)19.7 in
C)29.7 in
D)150.2 in
E)56.6 in

Question 21

Find the exact value of the function. sec

A)
B)
C)
D)
E)

Question 22

Find an approximate value of the function. Round your answer to the nearest ten-thousandth. cot 2.58

A)1.8778
B)0.6292
C)-0.6292
D)-1.1815
E)-1.5894

Question 23

Find two values of q , 0 q 360 that satisfy the given trigonometric equation.

A)315 ° , 225 °
B)45 ° , 315 °
C)315 ° , 135 °
D)45 ° , 135 °
E)135 ° , 225 °

Question 24

State the period of the function. csc t

A)2 p
B)
C)p
D)
E)3 p

Question 25

Perform the indicated operation and simplify.

A)1
B)
C)
D)
E)

Question 26

Use the unit circle below to find all real numbers t between 0 and 2 p for which sin t = 0.3. Estimate answer to the nearest tenth.

A)1.9, 4.4
B)1.3, 5.0
C)3.4, 6.0
D)6.0, 1.9
E)0.3, 2.8

Question 27

Use the unit circle below to find all real numbers t between 0 and 2 p for which cos t = 0.9. Estimate answer to the nearest tenth.

A)0.5, 5.8
B)4.3, 5.2
C)2.0, 0.5
D)2.7, 3.6
E)1.1, 2.0

Question 28

Use the unit circle below to estimate cos 3.3 to the nearest tenth.

A)3.3
B)0.2
C)-0.2
D)-1.0
E)1.0

Question 29

Approximate the given trigonometric function to six significant digits. tan 124 °

A)-10.7321
B)10.7321
C)1.48256
D)-0.674509
E)-1.48256

Question 30

Find the exact value of the expression. sin 330 ° - cos 300 ° tan 315°

A)-0.5
B)-1
C)0
D)0.5
E)0.25

Question 31

Use the unit circle below to estimate sin 4.9 to the nearest tenth.

A)1.0
B)0.2
C)4.9
D)-0.2
E)-1.0

Question 32

Determine whether the function is even, odd, or neither. v(x)=

A)Even
B)Odd
C)Neither

Question 33

Find two values of q 0, 2 p that satisfy the given trigonometric equation.

A)
B)
C)
D)
E)

Question 34

Find the exact value of the function.

A)undefined
B)0.5
C)0
D)-1
E)1

Question 35

Complete the identity. = ?

A)
B)
C)cot t
D)
E)

Question 36

Write the expression in terms of a single trigonometric function or a constant.

A)
B)
C)
D)
E)

Question 37

Determine whether the function is even, odd, or neither. H ( x )= , x 0

A)Even
B)Odd
C)Neither

Question 38

Evaluate W ( t )for the given t . t =

A)
B)
C)
D)
E)

Question 39

Write the expression in terms of a single trigonometric function or a constant.

A)
B)
C)
D)1
E)

Question 40

Perform the indicated operation and simplify.

A)
B)1
C)
D)
E)

Question 41

State the period of the function.

A)
B)p
C)5 p
D)
E)3 p

Question 42

Graph the function by using translations.

A)
B)
C)
D)
E)

Question 43

State the period of the function.

A)2 p
B)
C)
D)9 p
E)

Question 44

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs at t = 0. Frequency = 1.2 cycles per second, amplitude = 5 centimeters

A)
B)
C)
D)
E)

Question 45

Graph the function.

A)
B)
C)
D)
E)

Question 46

Find the amplitude, phase shift, and period for the graph of the function.

A)amplitude = 1, phase shift = 3 p , period =
B)amplitude = 3, phase shift = , period =
C)amplitude = 3, phase shift = , period = 2 p
D)amplitude = 3, phase shift = 3 p , period = p
E)amplitude = 3, phase shift = , period = 2 p

Question 47

State the amplitude and period of the function defined by the equation.

A)amplitude = 1.5 p , period = -2
B)amplitude = 2, period = 0.375 p
C)amplitude = 2, period = 1.5 p
D)amplitude = -2, period = 0.75 p
E)amplitude = 2 p , period = 1.5

Question 48

Find the amplitude, period, and frequency of the simple harmonic motion.

A)amplitude = 6 p , period = 2, frequency =
B)amplitude = 6, period = 2 p , frequency =
C)amplitude = , period = , frequency = 2 p
D)amplitude = 6, period = 2, frequency =
E)amplitude = p , period = , frequency = 2

Question 49

Graph the given function by using the addition-of-ordinates method.

A)
B)
C)
D)
E)

Question 50

Assume that a mass of m pounds on the end of a spring is oscillating in simple harmonic motion. What will be the effect on the period of the motion if the mass is increased to 25 m ?

A)The new period will be the same as the original period.
B)The new period will be 24 larger than the original period.
C)The new period is 25 times the original period.
D)The new period is 5 times the original period.
E)The new period will be 10 times larger than the original period.

Question 51

State the values for which the function is undefined.

A)
B)
C)
D)
E)

Question 52

Find the amplitude, period, and frequency of the simple harmonic motion.

A)amplitude = 9, period = p , frequency =
B)amplitude = 9, period = , frequency = p
C)amplitude = 9, period = , frequency =
D)amplitude = 2, period = 2 p , frequency =
E)amplitude = 2, period = , frequency = 2 p

Question 53

Use the information below to find cos t given .

A)
B)
C)
D)
E)

Question 54

Find the phase shift and the period for the graph of the function.

A)phase shift = , period =
B)phase shift = , period =
C)phase shift = , period =
D)phase shift = , period =
E)phase shift = , period =

Question 55

Graph the function defined by the equation.

A)
B)
C)
D)
E)

Question 56

Graph the function defined by the equation.

A)
B)
C)
D)
E)

Question 57

Graph the function defined by the equation.

A)
B)
C)
D)
E)

Question 58

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs when t = 0. Amplitude = 3.5 inches, frequency 1.5 cycles per second

A)
B)
C)
D)
E)