A point P lies 10 units from the origin O, and OP makes an angle of 30° with the positive $x$-axis. The coordinates of P are:

The horizontal step is 10·cos30° = 5√3 and the vertical step is 10·sin30° = 5, so P = (5√3, 5) ≈ (8.66, 5) — wider than it is tall, as a shallow 30° demands. Swapping the two ratios gives (5, 5√3), which is the point at 60°; using the cosine for both coordinates gives (5√3, 5√3), a point on the 45° line; and (√3/2, 1/2) forgets to scale by the distance 10.