Convert Polar Coordinates To Rectangular Coordinates - Pre-Calculus

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Question

Convert the polar coordinates to rectangular coordinates:

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

Answer

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

$x=r\cos\theta$

$y=r\sin\theta$

Using the information given in the question,

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

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

The rectangular coordinates are

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