find a polar equation

Question

$xy=7$

we get:

$r(\cos(\theta)\sin(\theta))=7$

therefore the only logical equation that could possibly arise is:

$r=\frac{7}{\cos(\theta)\sin(\theta)}$

yet web assign said nope $#%& off. Am I missing something basic here or is web assign dead wrong?

Answer 1

$$xy=r\cos\theta r\sin \theta$$ $$r^2=\frac{7}{\cos(\theta)\sin(\theta)}$$ $$r^2=\frac{7}{\sin(2\theta)/2}$$ $$r^2=14\csc 2\theta$$