Factoring and Plotting a Polar Equation

[vvc531]

Homework Statement

The question is: Factor and Plot the polar equation
r^2-r+(1/4)sin^2 4 theta

Homework Equations

N/A

The Attempt at a Solution

I have no idea how to do this.

 

[ideasrule]

r^2-r+(1/4)sin^2 4 theta is not an equation because there's no equal sign. Is it supposed to equal 0? If so, do you know how to factor a quadratic equation?

 

[vvc531]

yes it equals 0
how am i supposed to factor this?

 

[HallsofIvy]

You can't. Are you sure it isn't $r^2- r(1/4)sin^2(4\theta)$?

 

[ideasrule]

You can factor it. Does it make sense that if a and b are the roots of the equation, r^2-r+(1/4)sin^2 4 theta can be factored into A(r-a)(r-b)? You can find a and b using the quadratic formula. You won't get a numerical answer, but you will get an expression for a and b in terms of theta.