Asked by Nick
Let the polar coordinates of the point (x, y) be (r, θ). Determine the polar coordinates for the point (2x, y)
Answers
Answered by
oobleck
For (x,y), we have
r^2 = x^2 + y^2
tanθ = y/x
Let the new point have polar coordinates (p,φ). Then
p^2 = (2x)^2 + y^2 = 4x^2 + y^2 = r^2 + 3x^2
tanφ = y/(2x) = 1/2 (y/x) = 1/2 tanθ
You can massage those into other forms, of course.
r^2 = x^2 + y^2
tanθ = y/x
Let the new point have polar coordinates (p,φ). Then
p^2 = (2x)^2 + y^2 = 4x^2 + y^2 = r^2 + 3x^2
tanφ = y/(2x) = 1/2 (y/x) = 1/2 tanθ
You can massage those into other forms, of course.
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