Polar Equations

By Ronald Aguilar

Here we are looking at polar equations. Polar equations are math functions in the form of using the polar coordinate system. The graph below is the form . As you can see it looks like a spiral. In order to graph these functions the points are in the form (r, ). r is the polar distance and is the polar angle.

Here is the equation below for the graph . This is an example of a cardioid, a certain curve to limacons. As you can see it has a heart shape.

Equations of cardioids have a and b, . When in degrees the angle ranges from 0 to 180 deg. or the angle can range from 0 to 2. The value a scales the curve and the addition or substraction sign denotes the orientation.

Lets see what happens if change the a and b variable.

There are different kinds of polar equations such as circles, limacons, cardiods, and etc...

We MUST use the following conversions to find a polar equation: , ,

In order to convert the equations from rectangular form(what does this mean) to polar form we must set solve r in terms of . We cannot divide the equation by r, we must factor. In order to convert the equations from polar form to rectangular form we must divide both sides of the equation by r but do not if there is an trigonometric function in the denominator. Next, we square both sides if there is r and a constant.

In order to help graph polar equations there are three different types of symmetry that must be noted and examined. This symmetry along the x-axis, y-axis, and the origin. So the polar axis, the line , and the pole.

Equations of limacons cannot have a and b equal to zero.

Rose petal curves have the equations in form of or .