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 2-22:
Figure 2-22.-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
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
as the equation in rectangular coordinates.