Solving a Polar Plot with r^2 Area Problem: r^2=8cos(2θ)

[EvenSteven]

Area problem regarding r^2=8cos(2θ) and some other curve.

I don't understand how to plot this. I started off with a table of values. I get confused when θ = π/2. I thought it would give r^2 = -8. But looking at mathematica it gives a leminiscate that crosses the origin. How come? Is it because it would give imaginary values? Should I even take the square root? I was doing fine when it was just r = whatever.

Thanks.

 

[Dick]

Area problem regarding r^2=8cos(2θ) and some other curve.

I don't understand how to plot this. I started off with a table of values. I get confused when θ = π/2. I thought it would give r^2 = -8. But looking at mathematica it gives a leminiscate that crosses the origin. How come? Is it because it would give imaginary values? Should I even take the square root? I was doing fine when it was just r = whatever.

Thanks.

You can't get any point for the curve where r^2 is a negative number. Just plot over values of theta that give you a nonnegative number.