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

𝑥 0 𝜋 6 𝜋 4 𝜋 3 9 𝜋 1 9 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋
t a n 𝑥 0 1 3 1 3 12.1 3 1 1 3 0

Table B

𝑥 9 𝜋 1 9 𝜋 3 𝜋 4 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 9 𝜋 1 9
t a n 𝑥 1 2 . 1 3 1 1 3 0 1 3 1 3 12.1
  • 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