who invented polar coordinate grids?

Answer 1

Check the wiki about this. Here's an excerpt:

Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts at about the same time. Saint-Vincent wrote about them privately in 1625 and published in 1647, while Cavalieri published in 1635 with a corrected version appearing in 1653. Cavalieri first utilized polar coordinates to solve a problem relating to the area within an Archimedean spiral. Blaise Pascal subsequently used polar coordinates to calculate the length of parabolic arcs. In Method of Fluxions (written 1671, published 1736), Sir Isaac Newton was the first to look upon polar coordinates as a method of locating any point in the plane. Newton examined the transformations between polar coordinates and nine other coordinate systems. In Acta eruditorum (1691), Jacob Bernoulli used a system with a point on a line, called the pole and polar axis respectively. Coordinates were specified by the distance from the pole and the angle from the polar axis. Bernoulli's work extended to finding the radius of curvature of curves expressed in these coordinates. The actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th century Italian writers.

Answer 2

r² = x² + y² = (-5)² + (-5)² = 50 ==> r = ±?50 = ±5?2 tan? = y/x = (-5)/(-5) = a million ==> ? = ?/4 or ? = -3?/4 rcos? = x = (-5) ==> rcos? < 0 (a) rcos? < 0 and r > 0 ==> cos? < 0 ==> ? = -3?/4 (b) rcos? < 0 and r < 0 ==> cos? > 0 ==> ? = ?/4 The polar coordinates of the given element are (r = 5?2, ? = -3?/4) or (r = -5?2, ? = ?/4)

Answer 3

I think this is the answer you're looking for:
http://en.wikipedia.org/wiki/Polar_coordinates