Let a polar curve be described by r = f() and let be the line tangent
Question:
Let a polar curve be described by r = f(θ) and let ℓ be the line tangent to the curve at the point P(x, y) = P(r, θ) (see figure).
a. Explain why tan α = dy/dx.
b. Explain why tan θ = y/x.
c. Let φ be the angle between ℓ and the line through O and P. Prove that tan φ = f(θ)/f'(θ).
d. Prove that the values of θ for which ℓ is parallel to the x-axis satisfy tan θ = -f(θ)/f'(θ).
e. Prove that the values of θ for which ℓ is parallel to the y-axis satisfy tan θ = f'(θ)/f(θ).
Transcribed Image Text:
УА Ф r = f(0) Р(х, у) %3D Р(r, ө) ө х
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a The slope of the line tangent to r f0 at P is d Also the slope ...View the full answer
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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