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Find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3.
Solution:
The polar coordinate 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 (1, π/3)
When r is positive, the polar coordinate is (1, π/3 + 2nπ)
When r is negative, the polar coordinate is (-1, (2n + 1)π)
Therefore, all polar coordinates of the given point are (1, π/3 + 2nπ) and (-1, (2n + 1)π).
Find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3.
Summary:
All polar coordinates of point p where p = ordered pair 1 comma pi divided by 3 are (1, π/3 + 2nπ) and (-1, (2n + 1)π).
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