What are the components of the vector between the origin and the polar coordinate $(-1, (3pi)/4)$ ?

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Answer 1 · 2018-01-17T11:24:48

$[ sqrt(2)/2, -sqrt(2)/2 ]$

We can use $x=rcos(theta)$ and $y=rsin(theta)$ to convert:

$x=-1cos((3pi)/4)=-1(-sqrt(2)/2)=sqrt(2)/2$
$y=-1sin((3pi)/4)=-1(sqrt(2)/2)=-sqrt(2)/2$

So the vector is $[ sqrt(2)/2, -sqrt(2)/2 ]$ .

What are the components of the vector between the origin and the polar coordinate (-1, (3pi)/4)(-1, (3pi)/4)?