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.

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

    a) 1
    b) -1
    c) π
    d) 2π


  2. Question 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


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

    a) 3
    b) -3
    c) π
    d) 2


  4. Question 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)


  5. Question 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]


  6. Question 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


  7. Question 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]


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

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


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

    a) 0.5
    b) 2 π
    c) π / 2
    d) π


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

    a) √2
    b) √2 / 2
    c) 2 √2
    d) 2


ANSWERS
  1. a)
  2. b)
  3. a)
  4. c)
  5. d)
  6. b)
  7. b)
  8. c)
  9. d)
  10. a)