Polar Coordinates: Area: Example 1: r = cos 2ϴ

over 2 years ago

In this video I go further into determining the area of polar curves and this time do an example on evaluating the area of one loop of a 4 leaved rose given by the polar curve y = cos 2ϴ. I had graphed this curve in my Example 8 video, and I use the fact that one of the loops is bounded by the angles -π/4 and π/4. Thus we can apply the formula for area I derived in my last video, or remember the fact that the formula was derived by summing up an infinite amount of sectors of a circle, which we know the formula for as ½ r2ϴ. I also use symmetry to simplify the resulting integral and show that the area of one of the loops is π/8, thus the full curve is four times that, π/2. This is a very useful video in applying the area formula for polar curves so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvU1cfT6XTWOuHvAjw

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-area-example-1-r-cos-2

Related Videos:

Polar Coordinates: Area Formula: https://youtu.be/wd-EwiKzqa0
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Area of a Sector of a Circle: Proof: https://youtu.be/lglnySF8DyY
Equation of a Circle and its proof: http://youtu.be/xMXYJ9UeF4I
Integration Overview: How are Riemann Sums, Antiderivatives, and Integrals Linked?: https://youtu.be/TGnnu1vnD_U
Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE .