Worksheet: Graphs of Trigonometric Functions

In this worksheet, we will practice graphing trigonometric functions, such as sine, cosine and tangent, and deducing 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:

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

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

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

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

Q7:

Identify the graph of 𝑦=𝑥cosec.

  • A
  • B
  • C
  • D
  • E

Q8:

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

Q9:

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

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

  • Acosine
  • Btangent
  • Csine

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

Q10:

Consider the following figures.

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

  • ATangent
  • BSine
  • CCosine

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

Q11:

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

Q12:

Consider the following figures.

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

  • ASine
  • BTangent
  • CCosine

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

Q13:

Consider the following figures.

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

  • Asine
  • Bcosine
  • Ctangent

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

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

Q14:

Which function is represented on the graph?

  • A𝑦=2𝑥sin
  • B𝑦=𝑥sin
  • C𝑦=𝑥cos

Q15:

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

  • A
  • B
  • C
  • D
  • E

Q16:

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

  • A
  • B
  • C
  • D
  • E

Q17:

Which function is represented on the graph?

  • A𝑦=𝑥cos
  • B𝑦=2𝑥sin
  • C𝑦=𝑥sin

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