Pure · Trigonometry
Chapter 1 · 3
The idea
Arc length and sector area
The radian formulas for arc length, sector area and segment area, where they come from, and using them in reverse — finding a radius or angle from a given perimeter or area, and the perimeters of sectors and segments.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Trigonometry
Arc length and sector area
The radian formulas for arc length, sector area and segment area, where they come from, and using them in reverse — finding a radius or angle from a given perimeter or area, and the perimeters of sectors and segments.
Why it works
What fraction of the circle?
This lesson is the payoff for learning radians at all: three circle formulas that are one-liners in radians and a mess in anything else. Radians make circle measurements clean because a radian is defined so that the arc length equals the radius times the angle — and everything here is just "what fraction of the whole circle is this sector?"A full turn is radians and sweeps the whole circumference . An angle is the fraction of a full turn, so the arc is that fraction of the circumference:
Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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