How can $(-pi, -3pi/4)$ be converted into rectangular coordinates?

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Answer 1 · 2018-02-12T17:05:30

$color(blue)((-pi-sqrt(2)/2,-pi-sqrt(2)/2)$

enter image source here

From the diagram we can see that point P has polar coordinates
$( r , theta )$ and Cartesian coordinates $(x,y)$ .

And $color(white)(88)x=rcos(theta)$ , $y = rsin(theta)$

$(x,y) -> (rcos(theta), rsin(theta))$

We can use this to convert polar coordinates to Cartesian coordinates.

$x =-picos((-3pi)/4)=-pi-sqrt(2)/2$

$y=-pisin((-3pi)/4)=-pi-sqrt(2)/2$

$:.$

$color(blue)((-pi-sqrt(2)/2,-pi-sqrt(2)/2)$

How can (-pi, -3pi/4)(-pi, -3pi/4) be converted into rectangular coordinates?