What is the Cartesian form of $(33,(3pi)/8)$ ?

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Answer 1 · 2017-06-26T14:36:23

$(12.629, 30.488)$

We're given a polar coordinate and asked to find the Cartesian (rectangular) form of the coordinate.

We can picture this coordinate point like a vector, where $33$ is its magnitude and $(3pi)/8$ is the angle.

The $x$ - and $y$ -coordinates of this point are given by

$x = 33cos((3pi)/8) = color(red)(12.629$

$y = 33sin((3pi)/8) = color(blue)(30.488$

The Cartesian form of this polar coordinate is thus

$(color(red)(12.629), color(blue)(30.488))$

What is the Cartesian form of (33,(3pi)/8)(33,(3pi)/8)?