>>117315
You need to know the polar coordinate equations.
http://mathworld.wolfram.com/PolarCoordinates.html

That's all you need to know for the first one.

For the second one, he takes arcsin of both sides.
arcsin(-1) is 3pi/2 + 2pi*k, so theta is (3pi/2 + 2pi*k)/3

1) r=2cos[theta]
r^2 = 2rcos[theta] <-- multiply r both sides
x^2+y^2 = 2x <-- left side: r^2 = x^2+y^2 (pythagoras) right side: rcos[theta] = x (cos[theta]= x/r)
...
After that it's algebra. I'm assuming hte previous part was what you didn't get.

>>117321
>>117320
Why did he add 1 after x^2-2x+y^2=0?

>>117324
was it to make (x-1)^2?

>>117324
Completing the square. Honestly anon if you don't know this and your midterm is tomorrow you're quite fucked.

http://www.themathpage.com/alg/complete-the-square.htm#complete

>>117328
no, i got it >>117326
was just making sure