Lesson Worksheet: Graphs of Trigonometric Functions Mathematics

In this worksheet, we will practice graphing trigonometric functions, such as sine and cosine, and deduce their properties.

Q1:

Assign each plot shown in the graph below to the function it represents.

  • Athe red plot: cosine, the blue plot: sine
  • Bthe red plot: sine, the blue plot: cosine
  • Cthe red plot: cosine, the blue plot: tangent
  • Dthe red plot: tangent, the blue plot: cosine
  • Ethe red plot: tangent, the blue plot: sine

Q2:

Find the maximum value of the function 𝑓(𝜃)=11𝜃sin.

Q3:

Which symmetry of the unit circle proves that the tangent function is odd?

  • Asymmetry about the origin
  • Bsymmetry about the 𝑦-axis
  • Csymmetry about the 𝑥-axis

Q4:

Which of the following is the graph of 𝑦=(𝑥)tan?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of these two value tables shows a domain of the tangent function that can be used to construct its inverse function?

Table A

𝑥0𝜋6𝜋4𝜋39𝜋192𝜋33𝜋45𝜋6𝜋
tan𝑥0131312.131130

Table B

𝑥9𝜋19𝜋3𝜋4𝜋60𝜋6𝜋4𝜋39𝜋19
tan𝑥12.131130131312.1
  • ATable A
  • BTable B

Q6:

Which of the following is the graph of 𝑦=𝑥tan?

  • A
  • B
  • C
  • D
  • E

Q7:

What is the domain of the function tan𝜋𝑥2 whose graph is shown?

  • Aodd integers
  • Beven integers
  • Call real numbers except even numbers
  • Dall real numbers
  • Eall real numbers except odd integers

Q8:

Consider the following figures (a) and (b).

Which function does the plot in the graph, figure (a), represent?

  • Acosine
  • Bsine

Assign each region of the plot in figure (a) with the corresponding quadrant of the unit circle in figure (b).

  • AA: IV, B: I, C: II, D: III
  • BA: II, B: III, C: IV, D: I
  • CA: I, B: II, C: III, D: IV
  • DA: III, B: IV, C: I, D: II
  • EA: I, B: II, C: IV, D: III

Q9:

Consider the following figures.

Which function does the plot in the graph, figure (a), represent?

  • ASine
  • BCosine

Assign each region of the plot in figure (a) with the corresponding quadrant of the unit circle in figure (b).

  • AA: I, B: II, C: III, and D: IV
  • BA: IV, B: I, C: II, and D: III
  • CA: II, B: III, C: IV, and D: I
  • DA: I, B: II, C: IV, and D: III
  • EA: III, B: IV, C: I, and D: II

Q10:

Which function does the plot shown in the graph represent?

  • Asine
  • Bcosine
  • Ctangent

Assign each region of the plot with the corresponding quadrant of the unit circle.

  • AA: I, B: II, C: IV, D: III
  • BA: I, B: II, C: III, D: IV
  • CA: III, B: IV, C: I, D: II
  • DA: II, B: III, C: IV, D: I
  • EA: IV, B: I, C: II, D: III

This lesson includes 27 additional questions and 171 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.