# 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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