Graphs of Trigonometric Functions: Questions and Answers

This page presents multiple-choice questions on the graphs of trigonometric functions. The questions focus on identifying the period of a graph and matching graphs with their corresponding trigonometric equations. Answers are provided at the bottom of the page.

Questions

Question 1

What is the period of the graph shown below?

Graph of a trigonometric function for period identification

a) \( \pi/3 \)
b) \( 5\pi/3 \)
c) \( 2\pi/3 \)
d) \( 2\pi \)

Question 2

Which of the functions below represents the graph shown?

Cosine graph identification question

a) \( y = -\cos(2x) \)
b) \( y = \cos(2x) \)
c) \( y = -\cos(x) \)
d) \( y = \cos(x) \)

Question 3

Which of the trigonometric functions corresponds to the graph shown below?

Trigonometric graph with amplitude 2

a) \( y = 2\sin(x/4) \)
b) \( y = 2\cos(4x) \)
c) \( y = 2\cos(x/4) \)
d) \( y = 2\sin(4x) \)

Question 4

Which of the functions below corresponds to the given graph?

Sine graph with period 1

a) \( y = -\sin(2\pi x) \)
b) \( y = \sin(2\pi x) \)
c) \( y = \cos(2\pi x) \)
d) \( y = -\sin(x) \)

Question 5

What is the period of the graph below?

Periodic trigonometric graph

a) 1
b) 2
c) \( \pi \)
d) \( 2\pi \)

Question 6

Find an appropriate function for the following graph.

Low amplitude trigonometric graph

a) \( y = 0.5\cos(4\pi x) \)
b) \( y = 0.5\sin(x/4) \)
c) \( y = 0.5\sin(4x) \)
d) \( y = 0.5\cos(4x) \)

Question 7

Which of the functions below corresponds to the given graph?

Trigonometric graph with phase shift

a) \( y = \sin(x/2 - 1/4) \)
b) \( y = \sin(\pi x/2 - \pi/4) \)
c) \( y = \cos(\pi x/2 - \pi/4) \)
d) \( y = \sin(\pi x/2) \)

Question 8

What is the period of the graph below?

Trigonometric graph with period 2pi

a) \( 5\pi/4 \)
b) \( \pi/4 \)
c) \( \pi \)
d) \( 2\pi \)


Answers

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

More References

More Trigonometry Problems and Tutorials