Deck 5: Trigonometric Functions of Real Numbers

Question 1

State the domain and range of the function.
y = tan

Domain = _____________
Range = _____________

Answer 1

Domain = all real number such that n
where n is an integer
Range = all real numbers

Question 2

State the domain of the function.
Y = tan

A)
B)
C)
D)

Answer 2

Question 3

State the domain and range of the function.
y = tan

Domain = _____________
Range = _____________

Answer 3

Domain = all real number such that where n is an integer
Range = all real numbers

Question 4

State the domain of the function.
Y = tan

A)
B)
C)
D)

Question 5

State the domain and range of the function.
y = cot

Domain = _____________
Range = _____________

Question 6

State the domain and range of the function.
Y = cot

A)
B)
C)
D)

Question 7

State the domain of the function.
Y = -3 sec (14 x)

A)
B)
C)
D)

Question 8

State the domain and range of the function.
y =

Domain = ___________
Range = _____________

Question 9

State the domain of the function.
Y =

A)
B)
C)
D)

Question 10

State the domain and range of the function.
y =

Domain = ___________
Range = _____________

Question 11

State the domain of the function.
Y =

A)
B)
C)
D)

Question 12

State the domain and range of the function.
y =

Domain = ___________
Range = _____________

Question 13

State the domain of the function.
Y =

A)
B)
C)
D)

Question 14

Graph the function y =

over the interval

.

Question 15

Match the graph of the function over the interval

To its equation.

A) y =
B) y =
C) y =
D) y =

Question 16

Graph the function y =

,

.

Question 17

Match the graph of the function to its equation.

A) y =
B) y =
C) y =
D) y =

Question 18

Graph the function y =

,

.

Question 19

Match the graph of the function to its equation.

A) y =
B) y =
C) y =
D) y =

Question 20

Graph the function y =

,

.

Question 21

Match the graph of the function to its equation.

A) y =
B) y =
C) y =
D) y =

Question 22

Graph the function y =

,

.

Question 23

Match the graph of the function to its equation.

A) y =
B) y =
C) y =
D) y =

Question 24

Graph the function y =

,

.

Question 25

Match the graph of the function to its equation.

A) y =
B) y =
C) y =
D) y =

Question 26

State the domain and range of the function.
y = -7 sec (4 x)
Domain = __________
Range = ___________

Question 27

The angle of elevation from the top of a building 60 ft tall to the top of another building 90 ft tall is $\pi$ /8. What is the distance between the buildings? Round to nearest ft.

Question 28

A lighthouse is located on a small island 3 miles offshore. If the length of light beam is determined by y = 3|sec $\pi$ t | miles. Find the length of the beam at t =

. Round to nearest tenth of a mile.

Question 29

Graph the function y =

over one period.

Question 30

Match the graph of the function over one period to its equation.

A) y =
B) y =
C) y =
D) y =

Question 31

Graph the function y =

, over one period.

Question 32

Graph the function y =

, over one period.

Question 33

Graph the function y =

, over one period.

Question 34

State the amplitude and period of the sinusoidal function.
y = 4 sin 7 x
Amplitude _________
Period ___________

Question 35

State the amplitude and period of the sinusoidal function.
y =

sin 20 x
Amplitude _________
Period ___________

Question 36

State the amplitude and period of the sinusoidal function.
y =

Amplitude _________
Period ___________

Question 37

State the amplitude and period of the sinusoidal function.
Amplitude _________
Period ___________

Question 38

State the amplitude and period of the sinusoidal function.
Amplitude is ________
Period is _________

Question 39

Graph the function

over one period.

Question 40

Graph the function

over one period.

Question 41

Graph the function y =

over one period.

Question 42

Graph the function y =

over one period.

Question 43

Find an equation of the graph.

A) y =
B) y =
C) y =
D) y =

Question 44

Graph the function y =

over one period.

Question 45

Graph the function y =

over one period.

Question 46

Graph the function y =

over one period.

Question 47

Graph the function y =

over one period.

Question 48

Graph the function

over the interval [-8π, 8π] where 4π is the period of the function.

Question 49

Graph the function

over the interval [-16, 16] where 8 is the period of the function.

Question 50

Graph the function

over the interval [-1.3, 1.3] where 0.7 is the period of the function.

Question 51

Graph the function

over the interval [-1/2π, 1/2π] where 1/4π is the period of the function.

Question 52

Find an equation of the graph.

Question 53

Find an equation of the graph.

A) y =
B) y =
C) y =
D) y =

Question 54

Find an equation of the graph.

Question 55

Find an equation of the graph.

A) y =
B) y =
C) y =
D) y =

Question 56

Find an equation for the graph.

Question 57

Find an equation for the graph.

A) y =
B) y =
C) y =
D) y =

Question 58

Find an equation of the graph.

Question 59

Find an equation of the graph.

A) y =
B) y =
C) y =
D) y =

Question 60

Find an equation for the graph.

Question 61

Find an equation for the graph.

A) y =
B) y =
C) y =
D) y =

Question 62

What is the frequency for the oscillation modeled by y = 5 sin

Frequency is __________ cycles per second

Question 63

What is the frequency for the oscillation modeled by y = 9 cos

Frequency is __________ cycles per second

A) Frequency is cycles per second
B) Frequency is 16 $\pi$ cycles per second
C) Frequency is cycles per second
D) Frequency is 8 $\pi$ cycles per second

Question 64

If a sound wave is represented by y =

, what is amplitude and frequency?
Amplitude is __________ cm
Frequency is __________ hertz

Question 65

If a sound wave is represented by y = 0.009 cos 880

T, what is the frequency?

A) Frequency is 440 hertz
B) Frequency is 880 hertz
C) Frequency is 440? hertz
D) Frequency is 880? hertz

Question 66

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

is the angle of the vertex of the cone, then
where
Vis the speed of the plane andMis themachnumber, then what is the speed of the plane if the plane is flying atmach2.6? Round to the nearest meter.Speed of the plane is __________ m/sec.

Question 67

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

Is the angle of the vertex of the cone, then
Sin

Where V is the speed of the plane and M is the mach number, then what is the speed of the plane if the plane is flying at mach 1.6?
Speed of the plane is __________ m/sec.

A) Speed of the plane is 528 m/sec.
B) Speed of the plane is 206 m/sec.
C) Speed of the plane is 0.005 m/sec.
D) Speed of the plane is 52.8 m/sec.

Question 68

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

is the angle of the vertex of the cone, then
sin

where V is the speed of the plane and M is the mach number, then what is the mach number if the plane is flying at 891 m/sec.?
mach number is __________ .

Question 69

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

Is the angle of the vertex of the cone, then
Sin

Where V is the speed of the plane and M is the mach number, then what is the mach number if the plane is flying at 924 m/sec.?
Mach number is __________ .

A) mach number is 2.8
B) mach number is 0.28
C) mach number is 28
D) mach number is 0.36

Question 70

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

is the angle of the vertex of the cone, then
where
Vis the speed of the plane andMis themachnumber, then what is the speed of the plane if the cone angle is 60°. Round to the nearest whole number.Speed of the plane is __________ m/sec^.

Question 71

When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If

Is the angle of the vertex of the cone, then
Where V is the speed of the plane and M is the
machnumber, then what is the speed of the plane if the cone angle is 60^o

Round to the nearest whole number.Speed of the plane is __________ m/sec^.

A) Speed of the plane is 660 m/sec.
B) Speed of the plane is 381 m/sec.
C) Speed of the plane is 165 m/sec.
D) Speed of the plane is 101 m/sec.

Question 72

A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple harmonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

where A is the amplitude, t is the time in seconds, m is the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if

Amplitude: _____cm.
Mass: ______ g.

Question 73

A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple hormonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

Where A is the amplitude, t is the time in seconds, m is the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if

Amplitude: _____cm.
Mass: ______ g.

A) Amplitude: 5.5 cm.; mass:g.
B) Amplitude: 5.5 cm.; mass:g.
C) Amplitude: 30.25 cm.; mass:g.
D) Amplitude: 30.25 cm.; mass: 77.44 g.

Question 74

State the amplitude, period, and phase shift of the function.
y =
Amplitude = ________
Period = __________
Phase Shift = _________

Question 75

State the amplitude, period, and phase shift of the function.

A) Amplitude = 2; period = 2 $\pi$ ; phase shift =
B) Amplitude = 2; period = 2; phase shift =
C) Amplitude = 2; period = 2 $\pi$ ; phase shift =
D) Amplitude = 2; period = 2, phase shift =

Question 76

State the amplitude, period, and phase shift of the function.
y =

Amplitude = ________
Period = __________
Phase Shift = _________

Question 77

State the amplitude, period, and phase shift of the function.
Y =

A)
B)
C)
D)

Question 78

State the amplitude, period, and phase shift of the function.
y =

Amplitude = ________
Period = __________
Phase Shift = _________

Question 79

State the amplitude, period, and phase shift of the function.
Y =

A)
B)
C)
D)

Question 80

State the amplitude, period, and phase shift of the function.
y =

Amplitude = ________
Period = __________
Phase Shift = _________