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What are the rectangular coordinates of the polar point with r equal to 6 and theta equal to pi?
AThe point (-6, 0)
BThe point (6, 0)
CThe point (0, 6)
DThe point (0, -6)
Answer & Solution
Correct answer: A. The point (-6, 0)
1. Use x equal to r cos theta and y equal to r sin theta.
2. The cosine of pi is negative 1, so x is 6 times negative 1, which is negative 6.
3. The sine of pi is 0, so y is 6 times 0, which is 0.
4. The point is therefore (-6, 0), a half turn from the polar axis.
5. Answering (6, 0) treats the cosine of pi as positive 1 and lands on the wrong side.
_Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.3 Polar Coordinates_