Question

How do you graph `r^2 = sin(2theta)`?

Answer 1

Explanation:

Try plotting with points.

Some easy points would be `(0,0)`, `(pi/12,+-1/sqrt2)`, `(pi/8,+-1/root(4)2)`, `(pi/6,+-root(4)3/sqrt2)`, `(pi/4,+-1)`, `((3pi)/8,+-1/root(4)2)`, `(pi/2,0)`.

From the equation, `sin(2theta)` cannot be negative, so `theta` is restricted to `0 <= theta<= pi/2` or `pi <= theta <= (3pi)/2`.

And most values of `theta` corresponds to a positive and a negative value of `r`, the graph should have rotational symmetry.

If a graphing program for cartesian is available, the cartesian equation is

`(x^2 + y^2)^2 = xy`