sketch the graph of the polar equation

Question

Sketch the graph of the polar equation r = 2 cos θ. (Hint: convert to Cartesian coordinates, then use complete the square to put the equation into a recognizable “standard form").

Answer 1

Here's the rectangular form if this helps:

r=2cosθ is the given equation

x=rcosθ

y=rsinθ

multiply both sides of equation 1 by r

r^2=2rcosθ

but rcosθ=x

substitute

r^2=2x

now r^2=x^2+y^2

substitute

x^2+y^2=2x

x^2-2x+y^2=0

complete the square

x^2-2x+1+y^2=1

(x-1)^2+y^2=1

Answer 2

Hello Chris,

You could graph this directly by plugging in values for Θ (such as 0, 30, 45, 60, 90, ... degrees) and figuring out r. Then you would plot each point on polar graph paper.

.

Whoever wrote the question wants you to change the equation to Cartesian (x, y) form. In that case, use

cos Θ = x/r . After that, do some algebra to make an equation with r². After that, change r² to x² + y² and you will have a Cartesian equation. (r² = x² + y² is just the Pythagorean Theorem.)