How does the arc length equal the radian measure of angle AOB ? (question 2 on page 271)

When a circle’s radius is 1, its arc lengths are equal to their radian measures.

The full circumference of a circle is 2\pi r. When r=1, the circumference is 2\pi—the same as the radian measure of a full circle.

Remember that arc length and central angle are proportional:

\dfrac{\text{measure of central angle}}{2\pi\text{ radians}}=\dfrac{\text{arc length}}{\text{circumference}}

When r=1 and the circumference is 2\pi, the denominators in that equation are equal, so the arc length will always equal the measure of the central angle in radians.

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