Polar Coordinates: Example 9: Cardioid: Part 2: Question A
In this video I go over Part 2 of Example 9 on Polar Coordinates, and this time continue on solving Question A of that Example. From Part 1 I derived the formula for slope of the tangent line dy/dx for the Cardioid r = 1 + sinϴ. In this Part 2, I use that derived formula to solve for the slope of the line tangent to the point on the Cardioid curve where ϴ = π/3. The slope turns out to be -1, and this can be visually seen by sketching a line tangent to the Cardioid. I also use a good trick to remember exact trigonometric ratios for the angle π/3, which is drawing an isosceles triangle with sides of equal length 2. From here we can easily derive the ratios for sin(π/3) and cos(π/3), which we can then plug into the dy/dx formula. This is a quick, yet very useful video in determining the slopes of tangents lines to polar curves, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvNv97zW2xW6-zX_Mw
View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-polar-coordinates-example-9-cardioid-part-2-question-a
Related Videos:
Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE
Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY
Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM
Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE
Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
Polar Coordinates: Example 3: Cartesian to Polar: https://youtu.be/mV-9KTQM-RU
Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Proof that Sum of Angles in ANY Triangle = 180 degrees: https://youtu.be/4bI3BXIe2k8 .
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: [email protected]
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
▶️ 3Speak
I don’t always find the slope of a tangent line to a polar curve but when I do I usually make use of some exact trig ratios ;)
View video notes on the Hive blockchain: https://peakd.com/@mes/video-notes-polar-coordinates-example-9-cardioid-part-2-question-a
Thank you for sharing this post on HIVE!
Your content got selected by our fellow curator tibfox & you received a little thank you upvote from our non-profit curation initiative. Your post will be featured in one of our recurring curation compilations which is aiming to offer you a stage to widen your audience within the DIY scene of Hive.
Next time make sure to post / cross-post your creation within the DIYHub community on HIVE and you will receive a higher upvote!
Stay creative & hive on!