convert the polar equation to rectangular form?

Question

convert the polar equation to rectangular form

r=3cosThaida

Answer 1

r = 3 cos θ
r^2 =3r cos θ
x^2 + y^2 = 3x
x^2 + y^2 - 3x = 0

If you prefer y as a function of x:
y = ±sqrt(3x-x^2)

Answer 2

Convert the polar equation to rectangular form.
r = 3cosθ
________

Remember the identities.

x = rcosθ
y = rsinθ
x² + y² = r²
_________

r = 3cosθ
r² = 3rcosθ
x² + y² = 3x
x² - 3x + y² = 0
(x² - 3x + 9/4) + y² = 9/4
(x - 3/2)² + y² = 9/4

This is the equation of a circle with center (3/2,0) and radius 3/2.

Answer 3

x=r cos(theta)
y=r sin(theta)
From polar to rectangular:
r=sqrt(x^2+y^2)
theta=arctan(y/x)
r=3 cos(theta)
sqrt(x^2+y^2)=3
square both sides
x^2+y^2=9 is the rectangular form.