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...)
(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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are
the variables is a polar equation.