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Radian Measure, Arc Length, and Area

Section 1.2

Angles and the Trigonometric Functions

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Figure 1.9

Radian Measure of Angles

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The radian measure of the angle in standard position is the directed length of the intercepted arc on the unit circle.

Radian Measure of Angles

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Conversion from degrees to radians or radians to degrees is based on

180 degrees = π radians.

Degree-Radian Conversion

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Figure 1.12

Radian Measure of Angles

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Figure 1.15

Radian Measure of Angles

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Figure 1.17

The length s of an arc intercepted by a central angle of radians on a circle of radius r is given by

s = r.

Arc Length of a Circle

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Figure 1.21

The area A of a sector with central angle (in radians) in a circle of radius r is given by

.2

2rA

Area of a Sector of a Circle