Circles You Can Aim, Segments You Can Time

You'll learnto parametrize circles you can aim and line segments you can time.

Cosine and sine already trace the unit circle; the rest is aiming. Scale them for a new radius, add constants to move the center, and clip the interval to draw only an arc. A line segment works the same way: start at one point and travel a fixed fraction of the way toward the other.

8 STEPS · 6 QUICK CHECKS · START · DIRECTION · EXTENT · v2

Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.

arrowheads show the direction of travel

Before you start

What you're looking at

A point moving around the unit circle, ready to be resized, recentered, and clipped.

The question

What do multiplying, adding to, and restricting t each do to the circle?

Watch for

Radius, center, and swept portion changing one at a time, and a segment drawn as start plus a fraction of the displacement.

Step 1 / 8