Free Printable Lesson 9.4 - Graphing Sine and Cosine Functions

1.

Where is the midline of this sine graph?

a)

y=3

b)

y=1

c)

y=0

d)

y=pi

2.

What is the amplitude of this cosine graph?

a)

3

b)

6

c)

0

d)

2

3.

Period is how long it takes to go from the y-axis starting point, to the end of the cycle. What do you think the period would be here?

a)

pi/6

b)

pi/3

c)

2pi/3

d)

pi

e)

2pi

4.

8. What is the period for y = 4cos(¹/₂x +π) - 2?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

5.

9. What is the amplitude for y = 4cos(¹/₂x +π) - 2?

a)

2

b)

pi/2

c)

pi

d)

4

6.

10. What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

7.

11. What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

8.

12. What is the vertical shift?

a)

Down 1

b)

Down 5

c)

Down 3

d)

Down 4

9.

14. What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

10.

13. What is the equation of the graph?

a)

y = -2 cos x - 3

b)

y = 3 cos x - 2

c)

y = -7 cos x - 3

d)

y = -3 cos x - 4

11.

The __________ measure the distance from the midline to the max or min of the function.

a)

Amplitude

b)

Phase Shift

c)

Vertical Translation

d)

Horizantal Translation

12.

The vertical stretch of the graph; distance between the midline and the max/min.

a)

Period

b)

Cycle

c)

Axis of Oscillation

d)

Amplitude

13.

The horizontal length required to complete one cycle.

a)

Period

b)

Cycle

c)

Axis of Oscillation

d)

Amplitude

14.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

15.

what is the period of y= -3sinx

a)

π

b)

2π

c)

3π

d)

4π

16.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

17.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

18.

What is the period of y = 4Cos(2x)?

a)

4π

b)

π

c)

2π

d)

π/2

19.

What is the amplitude and period of y = 2sin(πx)

a)

2 and 2

b)

π and 2

c)

2 and π

d)

2π and 2

20.

Which trig function does this graph represent?

a)

y=sin(x)

b)

y=cos(x)

c)

neither

21.

Which trig function does this graph represent?

a)

csc

b)

sec

c)

cos

d)

sin

22.

What is the period of the Ferris wheel?

a)

4

b)

6

c)

8

d)

16

23.

What is the amplitude of the function?

a)

2

b)

1

c)

3

d)

5

24.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

25.

What is the equation of the midline of the graph?

a)

y = -3

b)

y = 2

c)

y = -2

d)

y = 3

26.

What is the equation of the midline of the graph?

a)

y = -1

b)

y = 0

c)

y = 3

d)

y = -3

27.

What is the amplitude of the graph?

a)

1

b)

2

c)

-3

d)

4

28.

What is the period of the graph?

a)

π

b)

2π

c)

4π

d)

8π

29.

A complete cycle of the function $y=A\cos\left(Bx\right)+C$ is shown. What is the value of A?

a)

12

b)

-12

c)

24

d)

8

30.

A complete cycle of the function $y=A\cos\left(Bx\right)+C$ is shown. What is the value of B?

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{8}$

c)

$\frac{\pi}{2}$

d)

$\frac{8\pi}{3}$

31.

What are the Amplitude, Period and Midline of this sin graph?

a)

Amp = 3
Period = $2\pi$

Midline - y = -1

b)

Amp = 3

Period = $\pi$

Midline - y = 3

c)

Amp = 2
Period = $3\pi$
Midline - y = 0

d)

Amp = 2
Period = $2\pi$
Midline - y = 1

32.

What is the midline of the graph shown?

a)

$y=2$

b)

$y=-2$

c)

$y=6$

d)

$y=0$

33.

Which equation best represents the graph pictured above?

a)

$y=3\sin x+1$

b)

$y=3\cos x+1$

c)

$y=2\sin x+1$

d)

$y=2\cos x+1$

34.

What is the midline of $y=3\cos5x-2$

a)

$y=3$

b)

$y=\frac{5}{3}$

c)

$y=-2$

d)

$y=5$

35.

Period = _______

(Just type the number)

36.

Amplitude = _____

37.

Midline = ______

38.

period = ______

39.

y=_____

40.

Amplitude = _____

41.

Use desmos to find your answer.

_______ days

42.

Which trig function does this graph represent?

a)

y=sin(x)

b)

y=cos(x)

c)

neither

43.

Which trig function does this graph represent?

a)

csc

b)

sec

c)

cos

d)

sin

44.

Is this graph periodic?

a)

yes

b)

no

45.

What is the amplitude of the function?

a)

2

b)

1

c)

3

d)

5

46.

What is the equation of the midline of the graph?

a)

y = -3

b)

y = 2

c)

y = -2

d)

y = 3

47.

What is the equation of the midline of the graph?

a)

y = -1

b)

y = 0

c)

y = 3

d)

y = -3

48.

What is the amplitude of the graph?

a)

1

b)

2

c)

-3

d)

4

49.

What is the period of the graph?

a)

π

b)

2π

c)

4π

d)

8π

50.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

51.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

52.

What is the amplitude of this function?

a)

2

b)

2π

c)

-2

d)

1

53.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

54.

Which equation?

a)

y= -cos(2x)

b)

y= cos(2x)

c)

y= (1/2)cosx

d)

y= (-1/2)cosx

55.

A complete cycle of the function $y=A\cos\left(Bx\right)+C$ is shown. What is the value of A?

a)

12

b)

-12

c)

24

d)

8

56.

What are the Amplitude, Period and Midline of this sin graph?

a)

Amp = 3
Period = $2\pi$

Midline - y = -1

b)

Amp = 3

Period = $\pi$

Midline - y = 3

c)

Amp = 2
Period = $3\pi$
Midline - y = 0

d)

Amp = 2
Period = $2\pi$
Midline - y = 1

57.

What is the midline of the graph shown?

a)

$y=2$

b)

$y=-2$

c)

$y=6$

d)

$y=0$

58.

Which equation best represents the graph pictured above?

a)

$y=3\sin x+1$

b)

$y=3\cos x+1$

c)

$y=2\sin x+1$

d)

$y=2\cos x+1$

59.

What is the midline of $y=3\cos5x-2$

a)

$y=3$

b)

$y=\frac{5}{3}$

c)

$y=-2$

d)

$y=5$

60.

The horizontal length required to complete one cycle.

a)

Period

b)

Cycle

c)

Axis of Oscillation

d)

Amplitude

61.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

62.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

63.

What is the period?

a)

4π

b)

2π

c)

π

d)

8π

64.

What is the period of this graph?

a)

2π

b)

π/2

c)

π/4

d)

π

65.

The period of a function is

a)

how long one cycle is before the function repeats

b)

how high and low the function goes from the center line

c)

the range of the function

66.

Amplitude refers to....

a)

how high and low the function varies from the center line.

b)

the length of the function

c)

how often the function repeats

67.

Is following periodic?

a)

Yes

b)

No

Lesson 9.4 - Graphing Sine and Cosine Functions

Total questions: 67

Worksheet time: 2hrs 14mins

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