Polar and Rectangular

Graph using (r, θ) instead of (x, y)

To convert from polar to rectangles x = rcosθ y = rsinθ

To convert from rectangles to polar r = sqrtx^2+y^2 θ = tan^-1(y/x)

Ex 1. Give the polar coordinates for the point (3,4)

r = sqrt3^2 + 4^2 θ = tan^-1(4/3)

r = sqrt25 = +/-5 θ = 53.130° add 180° for the second point – 233.130°

(5, 53°7’48”) and (-5, 233°7’48”)

Ex 2. Give the rectangular coordinates for (3, 30°)

x = 3cos30° y = 3sin30°

x = 3(sqrt3/2) y = 3(1/2)

x = 3sqrt3/2 y = 3/2

(3sqrt3/2, 3/2)