How do you use polar coordinates in graphing?

Answer 1

In much the same way as you use rectangular coordinates.

With Cartesian or rectangular coordinates, you start from the origin and move a distance of x in the horizontal direction and then a distance of y in the vertical direction.

Using polar coordinates, you start from the origin along a ray inclined at an angle theta with the positive horizontal axis (clockwise from Eastwards), and you go a distance r along that ray.

In all but degenerate cases the Cartesian coordinates of (r, theta) are

x = r*cos(theta) and y = r*sin(theta)

while, conversely,

r = sqrt(x2 + y2) and theta = arctan(y/x).