Apply any trigonometric identities that will simplify the equation. For example:
Convert the circle r^2 - 4r*cos(t - pi/2) + 4 = 25 to rectangular coordinates.
Use the identity cos(t - pi/2) = sin(t).
r^2 - 4r*sin(t) + 4 = 25
Apply the formulas for converting rectangular to polar if it simplifies the equation. Replace every r in the polar function with sqrt(x^2 + y^2). For example:
r^2 - 4r*sin(t) + 4 = 25
y = r*sin(t)
r^2 - 4y + 4 = 25
Replace every remaining r in the polar function with sqrt(x^2 + y^2, and every remaining t with arctan(y/x) and simplify. For example:
r^2 - 4y + 4 = 25
(sqrt(x^2 + y^2))^2 - 4y + 4 = 25
x^2 + y^2 - 4y + 4 = 25
Convert to the general form of the equation for the given shape. For example:
Convert the circle r^2 - 4r*cos(t - pi/2) + 4 = 25 to rectangular coordinates.
In rectangular coordinates, the general form of a circle is (x - a)^2 + (y - b)^2 = r^2.
Complete the square on the y terms.
x^2 + (y^2 - 4y + 4) = 25
x^2 + (y - 2)^2 = 25