Polar coordinates in 2D

Introduction to Polar Coordinates

When referring to Polar coordinates in Linear Algebra, there is a vector or point on a two-dimensional system whose coordinates comprise magnitude and the angle respected to one direction. 

This means we can draw one vector on a plane by knowing the magnitude of the vector and its angle. The magnitude is the length of one vector from the pole which represent by R and the angle of the vector represent by θ.

 

Example 1: a vector with the coordinates (R = 3, θ = 45 or π/4) or (R = 3, θ = -315 or -7 π/4)

anti-clockwise for a positive angle and clockwise for a negative angle

Example 2: a vector with the coordinates (R = 3,  θ = 135 or 3π /4) or (R = 3,  θ = -225 or -5π /4)