# Worksheet: Parametric Equations and Curves in Two Dimensions

In this worksheet, we will practice graphing curves given by a pair of parametric equations in 2D.

**Q1: **

Anthony wants to graph the parametric equations and , where .

He has started to complete a table of values.

0 | 0.5 | 1 | 1.5 | 2 | |

−2 | −1 | 1 | 2 | ||

3 | 2.75 | −1 |

Find the values of , and .

- A , ,
- B , ,
- C , ,
- D , ,

Use the table of values to determine which of the following graphs is correct.

- A
- B
- C
- D

**Q2: **

David wants to graph the parametric equations and , where .

He has started to complete a table of values.

0 | |||||

2 | |||||

0 | 0 |

Work out the values of , and .

- A , ,
- B , ,
- C , ,
- D , ,

When David plots the coordinates on a graph, he is not entirely sure about the shape of the curve. What is the one thing he could do to find out more about the shape of the curve?

- ADavid could extend the value of to be greater than .
- BDavid could extend his table of values; for example, he could increase by increments of rather than .
- CDavid could extend the value of to be lower than 0.

**Q4: **

A particle following the parameterization , of the unit circle starts at and moves counterclockwise. At what values of is the particle at ? Give exact values.

- A , where is a nonnegative integer
- B , where is a nonnegative integer
- C , where is a nonnegative integer
- D , where is a nonnegative odd number
- E , where is a nonnegative integer

**Q5: **

A particle following the parameterization , of the unit circle starts at and moves counterclockwise for . For what values of is the particle below the -axis? Give exact values.

- A , with
- BFor all real numbers
- C , with
- D , with
- E , with

**Q7: **

Consider the parametric equations and , where . Which of the following is the sketch of the given equations?

- A
- B
- C
- D
- E

**Q8: **

Consider the parametric equations and , where . Which of the following is the sketch of the given equations?

- A
- B
- C
- D
- E

**Q10: **

Consider the parametric equations and , where . Which of the following is the sketch of the given equations?

- A
- B
- C
- D
- E

**Q11: **

- A
- B