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Graphing Trig Functions

Total questions: 35

Worksheet time: 33mins

Name
Class
Date
1.
Determine an equation for this graph:
a)
y=csc(x)
b)
y=sec(x)
c)
y=cot(x)
d)
y= tan(x)
2.
What is the amplitude of the graph? 
a)
1
b)
3
c)
6
d)
9
3.
What is the vertical shift? 
a)
Down 1
b)
Down 5
c)
Down 3
d)
Down 4
4.
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 
5.
What is the period of y = 4Cos(2x)?
a)
4π
b)
π
c)
2π
d)
π/2
6.
Which sinusoidal equation is correct for a graph with an amplitude of 4, a period of π, and contains the point (0, 0)?
a)
y=4sin(2πx)
b)
y=4sin(2x)
c)
y=4cos(2πx)
d)
y=4cos(2x)
7.
The vertical stretch of the graph; distance between the midline and the max/min.
a)
Period
b)
Cycle
c)
Axis of Oscillation
d)
Amplitude
8.

How many cycles are completed in 1 unit interval.

a)

Period

b)

Frequency

c)

Axis of Oscillation

d)

Amplitude

9.
The horizontal length required to complete one cycle.
a)
Period
b)
Cycle
c)
Axis of Oscillation
d)
Amplitude
10.

Which formula do you use to discover the Period for sin and cos functions?

a)

Period=2π/b

b)

Period=b/2π

c)

Period=b/π

d)

Period=π/b

11.

What is the period for y = 4cos1/2(x +2π) - 2?

a)

π/2

b)

π

c)

3π

d)

4π

12.

What is the phase shift for y = 4cos1/2(x +2π) - 2?

a)

left π/2

b)

right π/2

c)

right 2π

d)

left 2π

13.

What is the vertical shift for y = 4cos1/2(x +2π) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

14.
Write an equation for the cosine function with amplitude 3, period 2π, phase shift of π, and vertical shift of 5.
a)
y = 5cos(x - π) + 3
b)
y = 3cos(x - π) + 5
c)
y = 3cos(2x - π) + 5
d)
y = 5cos(2x - π) + 3
15.
What is the equation of graph? 
a)
y = sin 5x
b)
y =  cos 5x
c)
y = 5 sin x
d)
y = 5 cos x 
16.
Determine an equation for this graph:
a)
y=csc(x)
b)
y=sec(x)
c)
y=cot(x)
d)
y= tan(x)
17.
Which value represents a vertical shift in the following function y=a*sin(bx - c)+d?
a)
a
b)
b
c)
c
d)
d
18.
Sine or Cosine?
a)
y=sinx
b)
y=cosx
19.
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
20.
Where does the graph of y = cos x begin?
a)
(0,0)
b)
(0,1)
c)
(0, Pi)
d)
(1, Pi)
21.
Where does the graph  y = sin x begin?
a)
(0,0)
b)
(0,1)
c)
(0, Pi)
d)
(1, Pi)
22.
What is the period?
a)
π/4
b)
π/2
c)
3π/4
d)
π
23.
What is the phase shift of the following
-3 tan (x) +1
a)
none
b)
-3
c)
up 1
d)
2π
24.
What is the vertical shift of the following
-3 tan (x) +1
a)
up 1
b)
1
c)
down 1
d)
-3
25.
How do you find the period of a transformed tangent graph?
a)
π/b
b)
2π/b
c)
2π
d)
b
26.
What is the period?
a)
4π
b)
2π
c)
π
d)
8π
27.
Which function below matches this graph?
a)
-cos4(x)
b)
sin4(x-1)
c)
1/4cos(x)+1
d)
1/4sin(x)+1
28.
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 
29.

What are the domain and range of both y=sin(x) and y=cos(x)?

a)

D: (-∞, ∞)

R: [-1, 1]

b)

D: (-∞, ∞)

R: [-π, π]

c)

D: (∞, -∞)

R: [-1, 1]

d)

D: (-∞, ∞)

R: [-∞, ∞]

30.
What is the equation of the graph shown?
a)
y=1/2cos2x
b)
y=1/2sin4x
c)
y=1/2cos4x
d)
y=4cos1/2x
31.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

32.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

33.

What is the period of the following:

2csc(6x)+1

a)

360 degrees

b)

30 degrees

c)

60 degrees

d)

2160 degrees

34.

What is the period of the following:

cot(2(x-5))

a)

360 degrees

b)

180 degrees

c)

90 degrees

d)

720 degrees

35.

Describe the transformation from the parent function of tan(x).

a)

Vertically compressed by 2 and vertical shift down 1

b)

Vertically compressed by 2 and horizontal shift right 1

c)

Vertically stretched by 2 and vertical shift down 1

d)

Vertically stretched by 2 and horizontal shift right 1

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