Find Horizontal/Vertical Tangents of Polar Curve r=cos(theta)+sin(theta)

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Discussion Overview

The discussion revolves around finding the points on the polar curve defined by r=cos(θ)+sin(θ) where the tangent lines are horizontal or vertical. Participants explore the necessary derivatives and conditions for determining these tangents within the interval 0 ≤ θ ≤ π.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant seeks assistance in finding horizontal and vertical tangents for the polar curve and mentions the need to convert polar coordinates to Cartesian coordinates.
  • Another participant introduces a theorem regarding the slope of the tangent line in polar coordinates and provides a formula for calculating it.
  • Several participants compute the derivative f′(θ) and discuss the conditions for horizontal tangents, specifically that the slope must equal zero.
  • There is a discussion about applying trigonometric identities to simplify expressions related to the tangent conditions.
  • Participants express uncertainty regarding the application of trigonometric identities and the correct manipulation of terms in their calculations.
  • One participant attempts to derive solutions for θ based on the conditions for horizontal tangents, while others question the correctness of their steps.
  • For vertical tangents, participants discuss the necessary condition involving the derivative and explore how to solve it, leading to further questions about identities and transformations.

Areas of Agreement / Disagreement

Participants generally agree on the need to find conditions for horizontal and vertical tangents, but there is no consensus on the specific steps or identities to use in their calculations. Uncertainty remains regarding the correct application of trigonometric identities and the manipulation of expressions.

Contextual Notes

Participants express limitations in their understanding of trigonometric identities and their applications, which may affect their ability to derive the necessary conditions for the tangents.

  • #31
Awesome, thank you so much! You've been a major help.
 
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  • #32
PullandTwist said:
Awesome, thank you so much! You've been a major help.

It is a pleasure to help someone who shows their work and makes a genuine effort. (Yes)

I look forward to seeing you around. :D
 

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