Determine two pairs of polar coordinates for the point 4
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Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°
Answered by admin @
Given coordinate points (x, y) = (4, -4) and it lies in IV quadrant.
tan θ = y/x = -4/4 = - 1.
We know that, tan θ is negative in II and IV quadrant.
In II quadrant, the angle θ = 3π/4.
In IV quadrant, the angle θ = 7π/4.
r2 = (x2 + y2) = (4)2 + (- 4)2 = 32
r = ± √(32) = ± 4√2.
Let us take positive value of r in IV quadrant (same quadrant)
. So, polar coordinates points will be (4√2, 7π/4).
Let us take negative value of r in II quadrant. So, polar coordinates points will be (-4√2, 3π/4).
Polar coordinates points of (4,-4) within the angle range of 0 to 360 degree are (4√2, 7π/4) and (-4√2, 3π/4).
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