# 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

**Q3: **

Which of the following is the graph of ?

- 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

0 | |||||||||

0 | 1 | 12.1 | 0 |

Table B

0 | |||||||||

0 | 1 | 12.1 |

- ATable A
- BTable B

**Q5: **

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q7: **

Identify the graph of .

- A
- B
- C
- D
- E

**Q8: **

Find the maximum value of the function .

**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).

- A: IV, : I, : II, : III
- B: II, : III, : IV, : I
- C: I, : II, : III, : IV
- D: III, : IV, : I, : II
- E: I, : II, : IV, : 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).

- A: I, : II, : III, : IV
- B: III, : IV, : I, : II
- C: II, : III, : IV, : I
- D: IV, : I, : II, : III
- E: I, : II, : IV, : III

**Q13: **

Consider the following figures.

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

- Asine
- Bcosine
- Ctangent

- 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

**Q15: **

Which of the following is the graph of ?

- A
- B
- C
- D
- E

**Q16: **

Which of the following is the graph of ?

- A
- B
- C
- D
- E