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.
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.
Convert into cartesian form.
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.