Click to copy, then share by pasting into your messages, comments, social media posts and websites.
Click to copy, then add into your webpages so users can view and engage with this video from your site.
Report Content
We also accept reports via email. Please see the Guidelines Enforcement Process for instructions on how to make a request via email.
Thank you for submitting your report
We will investigate and take the appropriate action.
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 the Notes on Steemit: https://steemit.com/mathematics/@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
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: http://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:
Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]
Try our 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
Try our Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
Category | Education |
Sensitivity | Normal - Content that is suitable for ages 16 and over |
Playing Next
Polar Coordinates: Example 9: Cardioid: Part 3: Question B
6 years, 3 months ago
Related Videos
Rational and Algebraic Functions - A Brief Explanation
2 days, 13 hours ago
Acids and Bases: Brønsted–Lowry, Arrhenius, and Lewis Models
3 days, 19 hours ago
Organic Compounds: Carbohydrates or Saccharides
4 days, 8 hours ago
Chemical Basis of Biology: Atoms, Molecules, and Electromagnetism
5 days, 6 hours ago
Introduction to Biology: Etymology and History
6 days, 8 hours ago
Warning - This video exceeds your sensitivity preference!
To dismiss this warning and continue to watch the video please click on the button below.
Note - Autoplay has been disabled for this video.