1 / 8

Differentiation in Polar Coordinates

Differentiation in Polar Coordinates. Lesson 10.7. Review. Relationship of polar and rectangular systems x = r cos θ y = r sin θ Given r = f( θ ), simple to find dr/d θ However, we seek dy/dx . Finding dy/dx. We know r = f( θ ) and y = r sin θ and x = r cos θ Then And .

kiana
Download Presentation

Differentiation in Polar Coordinates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Differentiation in Polar Coordinates Lesson 10.7

  2. Review • Relationship of polar and rectangular systems • x = r cos θ y = r sin θ • Given r = f(θ), simple to find dr/dθ • However, we seek dy/dx

  3. Finding dy/dx • We know • r = f(θ) and y = r sin θ and x = r cos θ • Then • And

  4. Finding dy/dx • Since • Then

  5. Example • Given r = cos 3θ • Find the slope of the line tangent at (1/2, π/9) • dy/dx = ? • Evaluate •

  6. Define for Calculator • It is possible to define this derivative as a function on your calculator

  7. Try This! • Find where the tangent line is horizontal for r = 2 cos θ • Find dy/dx • Set equal to 0, solve for θ

  8. Assignment • Lesson 10.7 • Page 443 • Exercises 1 – 21 odd

More Related