This is a free lesson from our course in Trigonometry In this lesson you'll learn; with the help of some examples, practice question with solution and video explanation by instructor on how to convert equation from polar form to the rectangular form. Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Equations in x and y are called rectangular (or Cartesian) equations and an equation where r and are the variables is a polar equation. (More text below video...)
Other useful lessons:
 Name Polar Coordinates Polar - Rectangular Coordinates Conversion
(Continued from above) You'll learn here, a polar equation can be converted to a rectangular equation using the formulas
r2 = x2 + y2
x = r cos y = r sin The steps to convert a polar equation to a rectangular equation will be to rearrange the equation so that the terms of the form r2, r cos or r sin appears suitably in the equation. Then we can substitute x2 + y2, x or y respectively.

For example, if you are to convert the polar equation r = 1/ (4 - 4 cos ) to rectangular form, first multiply both the sides by the denominator and get 4r - 4r cos = 1. Then add 4r cos on both the sides, that yields 4r = 1 + 4r cos . Square each side and substitute values of r2 and r cos in the resulting expression. You get the answer 16y2 = 8x + 1, which represents the equation of a parabola.

E.g. Convert the polar equation r = 4 sin to rectangular form.
Solution:
We multiply both sides by 'r',
r 2 = 4 r sin We now use the relationship between polar and rectangular coordinates:
r 2 = x 2 + y 2 and y = r sin to rewrite the equation as follows:
x 2 + y 2 = 4 y
x 2 + y 2 - 4 y = 0
It is the equation of a circle.

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