Videos and lessons to help High School students learn how to
derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define
the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.

Common Core: HSG-C.B.5

Arc Length of a Sector of a Circle using Radian Measurement

This video uses the definition of Radian measurement of angles in order to calculate the arc length of a sector of a circle.

Radians as Proportionality Constants

An angle measure in radians can be defined as the constant of proportionality in the relationship between the radius and the intercepted arc.

? = s/r

s = r ?

Arc Length and Area of a Sector

How to determine arc length and how to find the area of a sector.

A = 1/2 r

Radians, Arc Length & Sector Area

An introduction to the measure of radians and two commonly used radian formulas for the arc length and the sector area of a circle.

Investigate Area of a Sector and Arc Length

Rotate point C counterclockwise to change angle A, and move point B to change the radius.

1) What is the relationship between the circumference of the circle and 1 revolution? What is the relationship between the arc length s and the angle theta? Derive the equation.

2) What is the relationship between the area of the circle and 1 revolution? What is the relationship between the area of the sector and the angle theta? Derive the equation.

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