# 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 $s\hspace{0.17em}=\hspace{0.17em}2\pi r$ for a complete circle. Because $2\pi $ is the central angle (in radians) of the complete circle, the length `s` of any circular ...

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