The polar coordinates of a point are given. Find the rectangular coordinates of this point.
left parenthesis negative 3 comma negative StartFraction pi Over 6 EndFraction right parenthesis
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Part 1
What are the rectangular coordinates of this point?
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(Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
To convert from polar coordinates to rectangular coordinates, we use the formulas:
x = r * cos(theta)
y = r * sin(theta)
Given polar coordinates (-3, -pi/6), we have r = -3 and theta = -pi/6.
Substitute these values into the formulas:
x = -3 * cos(-pi/6) = -3 * sqrt(3)/2 = -3sqrt(3)/2
y = -3 * sin(-pi/6) = -3 * (-1/2) = 3/2
Therefore, the rectangular coordinates of this point are (-3sqrt(3)/2, 3/2).