Let a curve be described by r = f(), where f() > 0 on its domain. Referring
Question:
Let a curve be described by r = f(θ), where f(θ) > 0 on its domain. Referring to the figure of Exercise 62, a curve is isogonal provided the angle φ is constant for all θ.
a. Prove that φ is constant for all u provided cot φ = f'(θ)/f(θ) is constant, which implies that d/dθ (ln f(θ)) = k, where k is a constant.
b. Use part (a) to prove that the family of logarithmic spirals r = Cekθ consists of isogonal curves, where C and k are constants.
c. Graph the curve r = 2e2θ and confirm the result of part (b).
Data from Exercise 62
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Question Posted: