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 Video

Sample Question Videos

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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.