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
I’ve included another scenario below, this time with variable radius as well.
Variable Angle, Variable Radius
Explore changing polar coordinates here.
Connect your understanding of polar coordinates to that of cylindrical coordinates.
Thanks for reading.
samuelson mathxp 