Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
Solution:
The polar coordinates of any point can be written as
(r,θ) = (r, θ+2nπ) (when r is positive)
(r,θ) = (-r, θ+(2n+1)π) (when r is negative)
Where n is an integer.
Given the point is (5, π/3)
When r is positive, the polar coordinate is (5, π/3 + 2nπ)
When r is negative, the polar coordinate is (-5, (2n+1)π)
Therefore, all polar coordinates of a given point are (5, π/3 + 2nπ) and (-5, (2n+1)π).
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
Summary:
All polar coordinates of point p where p = ordered pair 5 comma pi divided by 3 is (5, π/3 + 2nπ) and (-5, (2n+1)π).
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