Radian, Arc Length and Sector Area
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 r2 ?
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.
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.