Polar Coordinates

Question

The rectangular coordinates of a point are given. Find polar coordinates ​(r,θ​)

of this point with θ expressed in radians. Let  r>0 and −2π<θ<2π.

​(2​,−2sq root of3​)

Answer 1

take the square root of the sum of squares of the x & y coordinates.

sqr(4+12) = sqr16 = 4 = r

the angle is -pi/3 or 5pi/3 = -60 degrees or 300 degrees

polar coordinates are (4,-pi/3) or (4,5pi/3)

It's the common 60 degree angle with sides of a right triangle in the ratio of 2-1-sqr3

but in Quadrant IV