Lesson: Conversion between Rectangular and Polar Equations Mathematics • Higher Education

In this lesson, we will learn how to convert equations from polar to rectangular form and vice versa.

Lesson Plan

Students will be able to

convert equations from polar to Cartesian form and vice versa,
recognize graphs of equations written in polar form by converting the equations to Cartesian form.

Lesson Video

Lesson Playlist

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01:54
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02:11

Lesson Worksheet

Q1:

Consider the polar equation . Complete the following steps to help you find the Cartesian form of the equation by writing an equivalent equation each time.

Multiply both sides of the equation through by .

Use the fact that to simplify the expression.

Given that and , we can use the Pythagorean theorem to show that . Use this to eliminate the in the previous expression.

Q2:

Convert into cartesian form.

Q3:

Consider the Cartesian equation .Complete the following steps to find the polar form of the equation by writing an equivalent equation each time.

First, use the fact that to eliminate .

Now, use the fact that to eliminate .

Finally, make the subject.