Question

What are the polar coordinates of the rectangular coordinates (2, -2√3)?

A. (4, 11π/6)
B. (4, 5π/3)
C. (2, 5π/3)
D. (2, 11π/6)
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Answer 1

9514 1404 393

Answer:

B. (4, 5π/3)

Explanation:

If you sketch the location of the point, you find the coordinates correspond to the side lengths of a 30°-60°-90° "special" triangle. The reference angle is 60°, or π/3 radians, and the magnitude of the vector is twice the short dimension, so is 2×2 = 4.

The polar coordinates are (4, 5π/3).