# Graphing r = 1 - cos(theta) (polar coordinates

• PsychonautQQ
In summary, the conversation discusses a graph that is difficult to interpret, particularly the way it bends around the y-axis. The speaker is able to easily graph r = sin(θ) but is having trouble with this particular graph. A plot for θ in the range of 0 to 2π is provided and the speaker points out that for θ = 0, cos(θ) = 1 and r = 0. As θ increases, cos(θ) decreases and r increases until θ = π, after which cos(θ) begins to increase again and r decreases until θ = 2π.

## Homework Statement

Okay the graph SHOULD look like this.
http://jwilson.coe.uga.edu/EMAT6680Fa11/Chun/11/21.png
I can't make sense of this at all. It looks so weird. Why does it bend around the y-axis in such an asymmetric way? I just graphed r = sin(θ) with ease by making a table of r vs θ
and graphing it... but this doesn't seem to be as easy?

A plot of the problem for ##\theta \in [0, 2\pi]## : http://gyazo.com/6811fa8ed2ba867fb9f16d49c3feea09

Notice for ##\theta = 0##, ##cos(\theta) = 1## so that ##r = 0##.

Now, as you increase ##\theta##, notice that ##cos(\theta)## will decrease until ##\theta = \pi## and ##r## will increase.

Then, ##cos(\theta)## begins to increase again and ##r## will start decreasing until ##\theta = 2\pi##.

## 1. What is the equation for graphing r = 1 - cos(theta) in polar coordinates?

The equation for graphing r = 1 - cos(theta) in polar coordinates is a polar form of a cardioid.

## 2. What does r = 1 - cos(theta) represent graphically?

Graphically, r = 1 - cos(theta) represents a heart-shaped curve with a single cusp at the origin.

## 3. What values of r and theta are allowed for graphing r = 1 - cos(theta)?

For r = 1 - cos(theta), r can take any positive value and theta can range from 0 to 2π.

## 4. How do I plot r = 1 - cos(theta) on a polar coordinate system?

To plot r = 1 - cos(theta) on a polar coordinate system, you can use a protractor to measure the angle and a ruler to measure the distance from the origin. Then, plot the points and connect them to create the curve.

## 5. What are some real-life applications of r = 1 - cos(theta) in polar coordinates?

One real-life application of r = 1 - cos(theta) in polar coordinates is in the design of roller coaster loops, as it represents the shape of a loop. It can also be used in engineering to model the path of a swinging pendulum or in astrophysics to describe the orbit of a planet around a star.