Determine Two Pairs Of Polar Coordinates For The Point (3, -3) With 0° ≤ Θ ≪ 360°.

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Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ 0 votescalculusaskedAug 4, 2014in CALCULUSby Tdog79Pupil
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The rectangular coordinate point : (x, y) = (3, -3).

You are watching: Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

The point (3, -3) lies in fourth quadrant.

tan θ = y/x = -3/3 = – 1.

The value of tan θ is negative in second and fourth quadrant.

In second quadrant, the angle θ = 3π/4.

In fourth quadrant, the angle θ =7π/4.

r2 = (x2 + y2) = (3)2 + (- 3)2 = 9 + 9 = 18.

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r = ± √(18) = ± 3√2.

Because θ was chosen to be in the same quadrant (fourth) as (x, y), we should be use a positive value of r.

The polar coordinates points is (3√2, 7π/4).

Because θ was not chosen to be in the same quadrant (second) as (x, y), we should be use a negative value of r.

The polar coordinates points is (-3√2, 3π/4).

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The polar coordinates points are (3√2, 7π/4) and (-3√2, 3π/4).

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