Lesson: Parametric Equations and Curves in Two Dimensions Mathematics • 12th Grade

In this lesson, we will learn how to graph curves given by a pair of parametric equations in 2D.

Lesson Plan

Students will be able to

sketch and identify graphs of parametric equations,
convert parametric equations into rectangular equations in order to sketch their graphs.

Lesson Video

Lesson Worksheet

Q1:

Noah wants to graph the parametric equations and , where .

He has started to complete a table of values.

Find the values of , and .

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

Q2:

Jackson wants to graph the parametric equations and , where .

He has started to complete a table of values.

Work out the values of , , and .

When Jackson 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?

Q3:

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.