The polar coordinates of a point are given. Find the rectangular coordinates of this point.

Question

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.)

Answer 1

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).