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Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ 0 votescalculusaskedAug 4, 2014in CALCULUSby Tdog79Pupil
Please log in or register to add a comment. Please log in or register to answer this question. 1 Answer 0 votes
The rectangular coordinate point : (x, y) = (3, -3).
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.
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).
The polar coordinates points are (3√2, 7π/4) and (-3√2, 3π/4).
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