Graphing polar equations with negatives?

Question

i don't know how to do r=3-2cos@ <-- unknown degrees.
I have no idea how the negative works when trying to graph the equation

Answer 1

When you graph in polar, you have 2 pieces information.

r = the radius (the distance from the origin)
@ = the angle (degrees around the axes, starting on the positive x, and rotating counterclockwise)

in your equation, give your @ a value. Example: 0.

r = 3 - 2cos(0) = 2. So the radius is 2 at angle 0.

If the radius (r) is negative, the distance from the origin is the absolute value of r but the angle is the exact opposite.

Example: if r = -2, and @ = 45 -- this is the same as r = 2, and @ = 225.

hope that helps

Answer 2

That's a limacon, a sort-of circle like thing with a loop in it. When the equation is positive cosine, the figure is to the right of the vertical axis, but with the negative sign, it's just flipped over to the left side. If you don't know how to sketch a limacon quickly, you can just plug in values and draw it by hand. You should go in 15 degree increments.

So, for example, plug in 15 degrees for theta.
r = 3 - 2cos(15)
r = 3 - 2(0.966)
r = 3 - 1.932
r = 1.068

Put a point at (1.068, 15)

Then plug in 30 degrees
r = 3 - 2cos(30)
r = 1.27

Put a point at (1.27, 30)

Continue all around the circle and connect the points along the way (make sure you connect them in order-- 15 to 30 to 45, etc.). That should give you a rough picture.

Or, if you have a graphing calculator, you can go to "mode" and change it from "func" to "pol" and graph it. Make sure it's in degrees, not radians!

Hope that helps. We just finished the polar equations unit in math class. :)

Answer 3

r = 3 - 2cosθ never goes negative. It has a minim of 1 and a maximum of 5

For those formulae where r does go negative plot |r| at θ ± 180°.