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TRANSFORMATION FROM POLAR TO CARTESIAN COORDINATES To transform to an equation in Cartesian or rectangular
coordinates from an equation in polar coordinates, use the following equations,
which can be derived from figure 222:
Figure 222.Polar to cartesian relationship. EXAMPLE:
Change the equation
to an equation in rectangular coordinates SOLUTION: Applying relations (2.14),
(2.15), and (2.16) to the above equation gives
Dividing both sides by _{
}we obtain
or y=x^{2} which is the equation we set out to find. EXAMPLE:
Change the following equation to an equation
in rectangular coordinates:
SOLUTION:
Written without a denominator, the polar
equation is
Using the transformations
we have y3x=3 as the equation in rectangular coordinates. 