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 r^{2
}= x^{2} + y^{2
}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 r^{2}, r cos
or r sin
appears suitably in the equation. Then we can substitute x^{2}
+ y^{2}, 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 r^{2} and r cos
in the resulting expression. You get the answer 16y^{2} = 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.
Winpossible's online math courses and tutorials have gained rapidly popularity since
their launch in 2008. Over 100,000 students have benefited from Winpossible's courses...
these courses in conjunction with free unlimited homework help serve as a very effective
mathtutor for our students.

All of the Winpossible math tutorials have been designed by topnotch instructors
and offer a comprehensive and rigorous math review of that topic.

We guarantee that any student who studies with Winpossible, will get a firm grasp
of the associated problemsolving techniques. Each course has our instructors providing
stepbystep solutions to a wide variety of problems, completely demystifying the
problemsolving process!

Winpossible courses have been used by students for help with homework and by homeschoolers.

Several teachers use Winpossible courses at schools as a supplement for inclass
instruction. They also use our course structure to develop course worksheets.