Distance and Direction

You'll learnto locate a point by distance and direction instead of across and up.

Rectangular coordinates say how far over and how far up. Polar coordinates say how far out and which way to face. The translation is right-triangle trigonometry, but two conventions carry the whole topic: a negative r walks you backward through the pole, and every point answers to infinitely many names.

8 STEPS · 6 QUICK CHECKS · RADIANS THROUGHOUT · v2

x = r cos θ · y = r sin θ

Before you start

What you're looking at

A point described two ways: rectangular (over then up) and polar (turn then move out), with the right triangle between them.

The question

How far out, and which way to face?

Watch for

The positive angle direction, degrees beside radians, and a negative r walking backward through the pole.

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