Find all polar coordinates of point p where p = (7, pi/3)
Solution:
The given coordinates (7, π/3)
Cartesian coordinates (x, y)=(7, pi/3)
The polar coordinates are (r, θ), where r = the directed distance from the pole of the unit circle and θ is the directed angle from the x-axis.
We need to find 4 possible polar coordinates for the point using radians.
Let us find 2 ordered pairs when r > θ
Add and subtract 2π to get the coterminal angles in the first quadrant.
π/3 + 2π = 7π/3 and
π/3 - 2π = -5π/3
They are (7,7π/3) and (7, -5π/3)
Let us find 2 ordered pairs when r < θ
Add and subtract 2π to get the coterminal angles in the third quadrant at 4π/3
4π/3 + 2π = 10π/3 and
4π/3 - 2π = -2π/3
They are (-7,10π/3) and (-7, -2π/3)
Hence, the polar coordinates are (7,7π/3), (7, -5π/3), (-7,10π/3) and (-7, -2π/3)
Find all polar coordinates of point p where p = (7, pi/3)
Summary:
The polar coordinates of point p where p =(7,7π/3), (7, -5π/3), (-7,10π/3) and (-7, -2π/3)
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