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Transformations of Trig Functions Worksheet

Transformations of Trig Functions Worksheet
  • Page 1
 1.  
Identify the equation for a cosine function of peroid 180°, after a phase shift 10° to the right.
a.
y = cos [2(θ - 10°)]
b.
y = cos θ + 10°
c.
y = cos θ - 10°
d.
y = cos [2(θ + 10°)]


Answer: (a)


Correct answer : (1)
 2.  
Identify the equation for a cosine function of peroid 45°, after a phase shift 60° to the left.
a.
y = cos [3(θ + 60°)]
b.
y = cos [8(θ + 60°)]
c.
y = cos [3(θ - 60°)]
d.
y = cos [8(θ - 60°)]


Answer: (b)


Correct answer : (2)
 3.  
Identify the equation for a sine function of peroid 45°, after a phase shift 35° to the left.
a.
y = sin [4(θ + 35°)]
b.
y = sin [4(θ - 35°)]
c.
y = sin [8(θ + 35°)]
d.
y = sin [8(θ - 35°)]


Answer: (c)


Correct answer : (3)
 4.  
Identify the equation for a sine function of peroid 90°, after a phase shift 50° to the left.
a.
y = sin [0.75(θ + 50°)]
b.
y = sin [4(θ - 50°)]
c.
y = sin [0.75(θ - 50°)]
d.
y = sin [4(θ + 50°)]


Answer: (d)


Correct answer : (4)
 5.  
A cosine graph with amplitude 4 and period 60° is translated 5 units down. Identify the equation of the graph after transformation.
a.
y = 4cos 6θ - 5
b.
y = 6cos 4θ + 1
c.
y = 4cos θ + 6
d.
y = 6cos 4θ - 5


Answer: (a)


Correct answer : (1)
 6.  
A cosine graph with amplitude 4 and period 180° is translated 1 unit down. Identify the equation of the graph after transformation.
a.
y = 4cos 2θ + 3
b.
y = 4cos 2θ - 1
c.
y = 2cos 4θ - 1
d.
y = 4cos 2θ + 1


Answer: (b)


Correct answer : (2)
 7.  
A sine graph with amplitude 1 and period 30° is translated 3 units up. Identify the equation of the graph after transformation.
a.
y = sin 8θ + 4
b.
y = sin 12θ + 3
c.
y = sin 3θ + 12
d.
y = sin 12θ - 3


Answer: (b)


Correct answer : (2)
 8.  
Identify the equation for a cosine function of peroid 180°, after a phase shift 10° to the right.
a.
y = cos [2(θ - 10°)]
b.
y = cos [2(θ + 10°)]
c.
y = cos θ - 10°
d.
y = cos θ + 10°


Answer: (a)


Correct answer : (1)
 9.  
Identify the equation for a cosine function of peroid 45°, after a phase shift 60° to the left.
a.
y = cos [8(θ + 60°)]
b.
y = cos [3(θ - 60°)]
c.
y = cos [3(θ + 60°)]
d.
y = cos [8(θ - 60°)]


Answer: (a)


Correct answer : (1)
 10.  
Identify the equation for a sine function of peroid 45°, after a phase shift 35° to the left.
a.
y = sin [4(θ - 35°)]
b.
y = sin [8(θ - 35°)]
c.
y = sin [8(θ + 35°)]
d.
y = sin [4(θ + 35°)]


Answer: (c)


Correct answer : (3)

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