Directions are simple either convert from polar to Cartesian or vice versa...

1. $\displaystyle r\sin(\theta - \frac{\pi}{4}) = 2$

Then....

$\displaystyle \sin(\theta - \frac{\pi}{4}) = \frac{\sqrt{2}}{2}(sin\theta - cos\theta)$

$\displaystyle x - y = 2\sqrt{2}$

$\displaystyle y = x - 2\sqrt{2}$

Now, my book has $\displaystyle y = x + 2\sqrt{2}$ and I just can't see how they got it, maybe I'm skipping something or making a mistake, but I can't see it as of now.

And...

2. $\displaystyle r^2\sin2\theta = 2$

I got it to...

$\displaystyle r = \frac{1}{xy}$

But that doesn't seem right, so there's probably something obvious I'm missing.

Also, as intuitive as it seems

$\displaystyle \theta = \frac{\pi}{2}$ and $\displaystyle \theta = \frac{3\pi}{2}$ are both $\displaystyle x = 0$

$\displaystyle \theta = \pi$ and $\displaystyle \theta = 0$ are both $\displaystyle y = 0$

Thanks for the help.