Show that if the polar graph of r = f( ) is rotated counterclockwisearound the origin
Chapter 10, Problem 65(choose chapter or problem)
Show that if the polar graph of \(r=f(\theta)\) is rotated counterclockwise around the origin through an angle \(\alpha\), then \(r=f(\theta-\alpha)\) is an equation for the rotated curve.
[Hint: If \(\left(r_{0}, \theta_{0}\right)\) is any point on the original graph, then \(\left(r_{0}, \theta_{0}+\alpha\right)\) is a point on the rotated graph.]
Equation Transcription:
Text Transcription:
r=f(theta)
r=f(theta-alpha)
(r_0,theta_0)
(r_0,theta_0+alpha)
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