You have a point on a rectangular graph with coordinates (6, 8).
You want to describe the same location in polar coordinates ... R and Θ .
-- 'R' is the distance from the origin to the point.
-- 'Θ' is the angle you'd need to turn the x-axis counterclockwise
around the origin to make it pass through the point.
To change rectangular coordinates to polar coordinates:
R = √(x² + y²)
Θ = the angle whose tangent is (y / x) .
(6i + 8j) is the [Cartesian] vector that takes you from the origin to (6, 8) .
R = √(6² + 8²) = √(36 + 64) = √100 = 10
Θ = tan⁻¹ (8/6) = 53.13° (rounded)
In polar coordinates, the same point is 10 ∠53.13° .
