# How do you graph #r=1-2costheta#?

##### 2 Answers

Please read the explanation.

#### Explanation:

We have the **Polar equation**:

**Polar Equations** are graphed on the two-dimensional **Polar Coordinate System**.

The point **distance from the origin**.

**angle** from the **positive x-axis**, measured **counter-clockwise**.

In the next step, we will create a **Data Table** of values for the **Polar equation**:

To calculate

The **Data Table** is below:

Use the table of values to generate the following graph:

Two graphs are drawn:

One for the **parent function**

and the other for

We can understand the behavior of the graph for

when we compare the two graphs:

Hope it helps.

I have used Socratic graphic facility that discards r-negative pixels.

#### Explanation:

The pole r = 0 is a node, with two distinctive tangents, in the

directions

anticlockwise sense ) and returning to the pole, theta =

In exactitude, the Cartesian equation is

x^2+y^2 = sqrt(x^2+y^2)+2x=0.

The Socratic graph is immediate, for

graph{x^2+y^2-sqrt(x^2+y^2)+2x=0[-5 5 -2.5 2.5]}.

See r-positive graph of r = - ( 1 + 2 cos theta )

graph{x^2+y^2+sqrt(x^2+y^2)+2x=0[-5 5 -2.5 2.5]}

See the r-positive combined graph for

graph{(x^2+y^2+2x)^2-(x^2+y^2)=0[-5 5 -2.5 2.5]}.

I use Mathematical graphic plotting, for