8.4 Applications of Radian Measure

  • Arc Length on a Circle • Area of a Sector of a Circle • Linear and Angular Velocity

Radian measure has numerous applications in mathematics and technology. In this section, we discuss applications involving circular arc length, the area of a sector, and the relationship between linear and angular velocity.

ARC LENGTH ON A CIRCLE

From geometry, we know that the length of an arc on a circle is proportional to the central angle formed by the radii that intercept the arc. The length of arc of a complete circle is the circumference. Letting s represent the length of arc, we may state that s = 2πr for a complete circle. Because 2π is the central angle (in radians) of the complete circle, the length s of any circular ...

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