Need some help here:
Transform the polar equation to rectangular coordinates and identify the curve represented by $$r = \sin t + \cos t$$
What I've done:
$$r^2 = r\sin t+r\cos t $$
$$x^2+y^2 = x + y$$
I'm kind of clueless on how to go from there though. Could anyone help?
$$x^2+y^2 = x + y \iff x^2 - x + y^2 - y =0 $$
Complete the squares, and you'll find you have a circle!
$$\left(x^2 - x + \frac 14\right) + \left(y^2 - y + \frac 14\right) = \frac 12$$
$$\left(x - \frac 12\right)^2 + \left(y - \frac 12\right)^2 = \left(\sqrt{\frac 12}\right)^2$$
It's a circle centered at $\left(\frac 12, \frac 12\right)$ of radius $\frac 1{\sqrt 2}$