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Precalculus : Convert Polar Coordinates To Rectangular Coordinates

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Example Question #1 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

$\left(5, \frac{3\pi}{2}\right)$ $\displaystyle \left(5, \frac{3\pi}{2}\right)$

Possible Answers:

(0, -5) $\displaystyle (0, -5)$

$\displaystyle (-5, -5)$

(-5, 0) $\displaystyle (-5, 0)$

(5, 0) $\displaystyle (5, 0)$

Correct answer:

(0, -5) $\displaystyle (0, -5)$

Explanation:

To convert polar coordinates $(r, \theta)$ $\displaystyle (r, \theta)$ to rectangular coordinates (x, y) $\displaystyle (x, y)$ ,

$x=r\cos\theta$ $\displaystyle x=r\cos\theta$

$y=r\sin\theta$ $\displaystyle y=r\sin\theta$

Using the information given in the question,

$x=5\cos \frac{3\pi}{2}=5(0)=0$ $\displaystyle x=5\cos \frac{3\pi}{2}=5(0)=0$

$y=5 \sin \frac{3\pi}{2}=5(-1)=-5$ $\displaystyle y=5 \sin \frac{3\pi}{2}=5(-1)=-5$

The rectangular coordinates are (0, -5) $\displaystyle (0, -5)$

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Precalculus : Convert Polar Coordinates To Rectangular Coordinates

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