Wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Graphing Trigonometric Functions

Total questions: 33

Worksheet time: 40mins

Name
Class
Date
1.
What is the equation of graph? 
a)
y = sin 5x
b)
y =  cos 5x
c)
y = 5 sin x
d)
y = 5 cos x 
2.
What is the vertical shift? 
a)
Down 1
b)
Down 5
c)
Down 3
d)
Down 4
3.
Determine an equation for this graph:
a)


y=csc(x)
b)


y=sec(x)
c)
y=cot(x)
d)


y= tan(x)
4.
What is the maximum value of the wave y = 10sin(2x - 20) + 25?
a)
10
b)
20
c)
35
d)
30
5.
The following wave represents a sound recorded for 8s.  Which equation best represents this wave?
a)
S = 5sin(2x)
b)
S = sin(5x) 
c)
S = 5sin(180x)
d)
S = 180sin(5x)
6.
Which is an equation of the cosine function with an amplitude of 2, period of Π, phase shift of Π/2?
a)
y= -2cos(x/2 - ∏/4)
b)
y= 2cos (x/2 + ∏)
c)
y= 2cos (2x-∏)
d)
y= -2cos(2x-∏/2)
7.
What is the phase shift for y = 4cos(1/2x +π) - 2?
a)
left pi/2
b)
right pi/2
c)
right 2pi
d)
left 2pi
8.
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 
9.
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 
10.
What is the period?
a)
π/4
b)
π/2
c)
3π/4
d)
π
11.

Describe the horizontal and vertical shifts.

a)

left π , up 4

b)

left π , down 3

c)

right π , up 4

d)

right π , down 3

12.

What is the period of the equation shown?

a)

3π

b)

2π

c)

3π / 2

d)

2π / 3

13.

What is the equation of the graph shown?

a)

y = 3sin(θ + π/4) - 1

b)

y = 3cos(θ - π/4) -1

c)

y = 3sin(θ - π/4) + 1

d)

y = 3cos(θ + π/4) + 1

14.

What is the equation for the graph shown.

a)

y = 4sinθ - 2

b)

y = 3tcosθ - 1

c)

y = 2tanθ - 4

d)

y = 2-4tanθ + 2

15.

What is the equation of the graph shown?

a)

y = tanθ/2

b)

y = tan2θ

c)

y = tanθ/4

d)

y = tan4θ

16.

What is the equation of the graph shown?

a)

y = 4cosθ/2 - 6

b)

y = 4cosθ/2 - 2

c)

y = -2cosθ/4 - 2

d)

y = 4cosθ/4 + 2

17.

What is the equation of the graph shown?

a)

y = -sinθ -1

b)

y = -sinθ/2 -1

c)

y = -2sin2θ + 1

d)

y = sinθ/2 + 1

18.

Describe the horizontal shift.

a)

left 3π / 4

b)

left 4π / 3

c)

right 3π

d)

right 3π / 4

19.

What is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

20.

Name the function and how many units the graph shifted vertically.

a)

sine, 2 units up

b)

cosine, 2 units down

c)

cosine, 2 units up

d)

sine, 2 units up

21.

Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

a)

y = 5cos(x - pi) + 3

b)

y = 3cos(x - pi) + 5

c)

y = 3cos(2x - pi) + 5

d)

y = 5cos(2x - pi) + 3

22.

1.      Find the phase shift of the graph of the function 
y=2cos⁡⁡6(x+π6)y=2\cos⁡6(x+\frac{\pi}{6})  

a)

π\pi units right

b)

π\pi units left

c)

π6\frac{\pi}{6}  units right

d)

undefined units left

23.

Where does the graph of cosine begin?

a)

(0,0)

b)

(0,1)

c)

(0, Pi)

d)

(1, Pi)

24.

Where does the graph of y=sin(x) begin its first cycle?

a)

(0,0)

b)

(1,0)

c)

(0,Pi)

d)

(1, Pi)

25.

What does cos(0)= ?

a)

1

b)

0

c)

-1

d)

Undefined

26.

What does sin(π) = ?

a)

1

b)

0

c)

-1

d)

Undefined

27.

What does tan(0) = ?

a)

1

b)

0

c)

-1

d)

Undefined

28.

What does sin(0) = ?

a)

1

b)

0

c)

-1

d)

Undefined

29.

What does tan(3π/4) =

a)

1

b)

0

c)

-1

d)

Undefined

30.
What is the domain and range of y=sinx?
a)
D: (-∞, ∞)
R: [-1, 1]
b)
D: (-∞, ∞)
R: [-
π, π]
c)
D: (∞, -∞)
R: [-1, 1]
d)
D: (-∞, ∞)
R: [-
∞, ∞]
31.

Which trigonometric functions have no amplitude?

a)

cotangent

b)

cosine

c)

secant

d)

tangent

e)

cosecant

32.

Which trig function is graphed above?

a)

secant

b)

cotangent

c)

cosecant

d)

tangent

33.

Which trig function is graphed above?

a)

cotangent

b)

tangent

c)

secant

d)

cosecant