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

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To find the horizontal and vertical tangents of the polar curve r=cos(θ)+sin(θ), the process involves converting polar coordinates to Cartesian coordinates and calculating the derivatives dy/dθ and dx/dθ. The slope of the tangent line is determined using the formula dy/dx = (dy/dθ)/(dx/dθ), requiring the numerator to be zero for horizontal tangents and the denominator to be zero for vertical tangents. The discussion highlights the use of trigonometric identities to simplify expressions, leading to solutions for θ at specific angles. Ultimately, the points corresponding to these angles are derived, providing insight into the behavior of the curve at these tangent points.
  • #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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