Question

How to get 6i and 8j in polar form

Answer 1

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°  .