Area of Circle (another perspective)

Posted: February 20, 2016 in Area, Calculus: An Introduction, Integral Calculus
Tags: , ,

Polar coordinates are not formally introduced in high school, yet sector area is required to prove fundamental trigonometric limits. Having already seen that proof, it wouldn’t be all that painful for students to see circle area derived through the limiting process as applied to angles.

Variable Angle Fixed Radius

Circle AreaPolar

 

I’ve included another scenario below, this time with variable radius as well.

Variable Angle, Variable Radius

 

Circle AreaPolar(delta r)

Explore changing polar coordinates here.

Connect your understanding of polar coordinates to that of cylindrical coordinates.

 

Thanks for reading.

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