# 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 .

Q3:

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

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

Q4:

Which of the following is the graph of ?

• 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

 𝑥 tan𝑥 0 𝜋6 𝜋4 𝜋3 9𝜋19 2𝜋3 3𝜋4 5𝜋6 𝜋 0 1√3 1 √3 12.1 −√3 −1 −1√3 0

Table B

 𝑥 tan𝑥 −9𝜋19 −𝜋3 −𝜋4 −𝜋6 0 𝜋6 𝜋4 𝜋3 9𝜋19 −12.1 −√3 −1 −1√3 0 1√3 1 √3 12.1
• ATable A
• BTable B

Q6:

Which of the following is the graph of ?

• A • B • C • D • E Q7:

What is the domain of the function 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.

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