Questions on Amplitude, Period, range and Phase Shift of Trigonometric Functions

Multiple choice questions on determining the amplitude, period, range and phase shift of trigonometric functions with answers at the bottom of the page.

Question 1

If y = cos x, then what is the maximum value of y?

a) 1
b) -1
c) π
d) 2π

Question 2

What is the period of the trigonometric function given by f(x) = 2 sin(5 x)?

a) π / 5
b) 2 π / 5
c) 5 π
d) π

Question 3

What is the amplitude of the function f(x) = -3cos(πx)?

a) 3
b) -3
c) π
d) 2

Question 4

Which of the following functions has the greatest period?

a) f(x) = 20 sin(2x-π/2)
b) f(x) = - sin(πx)
c) f(x) = 2 sin(0.1 x)
d) f(x) = - sin(0.1 π x)

Question 5

What is the range of the function f(x) = - 4 cos(2x - 3)?

a) (0 , 4)
b) [0 , 4]
c) (-4 , 4)
d) [-4 , 4]

Question 6

What is the phase shift of the function f(x) = 7sin(2x - π / 3)?

a) π / 3
b) π / 6
c) - π / 6
d) - π / 3

Question 7

What is the range of the function f(x) = - 6 cos(π x - π/2) + 2?

a) [-6 , 6]
b) [-4 , 8]
c) [0 , 8]
d) [-6 , 0]

Question 8

What is the amplitude of f(x) = 4 sin(x) cos(x)?

a) 4
b) 3
c) 2
d) 1

Question 9

What is the period of f(x) = 0.5 sin(x) cos(x)?

a) 0.5
b) 2 π
c) π / 2
d) π

Question 10

What is the amplitude of f(x) = sin(x) + cos(x)?

a) √2
b) √2 / 2
c) 2 √2
d) 2

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