How to graph the equation r = 1 + cos ( θ ) ?

Question

How to graph the equation       r    =    1    +          cos              (        θ        )            ?

wongmczuy · Accepted Answer

Here is a method to get the equation into rectangular form so you can graph it if you're trying to graph it in rectangular form.
We can make use of the following formulas when trying to convert from polar to rectangular:

x = r \cos (θ)

and

y = r \sin (θ)

r^{2} = x^{2} + y^{2}

Now we can rewrite our equation:

r = 1 + \cos (θ)

Multiplying both sides by

r

gives us

r^{2} = r (1 + \cos (θ))

= r + r \cos (θ)

Substituting the value of

r = \sqrt{x^{2} + y^{2}}

into our equation yields

r^{2} = r + r \cos (θ)

= \sqrt{x^{2} + y^{2}} + x

So our equation becomes

x^{2} + y^{2} = \sqrt{x^{2} + y^{2}} + x

, which is equivalent to

r = 1 + \cos (θ)

.
Below are a few graphs.
Graph of

x^{2} + y^{2} = \sqrt{x^{2} + y^{2}} + x

or

r = 1 + \cos (θ)

How to graph the equation r = 1 + cos( theta )?

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