What is the Cartesian form of $( 3 , (-9pi)/4 )$ ?

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Answer 1 · 2016-11-20T10:44:37

The cartesian coordinates are $((3sqrt2)/2,(-3sqrt2)/2)$

To convert from polar coordinates $(r,theta)$ to cartesian coordinates $(x,y)$ , we use the following equations

$x=rcostheta$

and $y=rsintheta$

Here $(r,theta)=(3,-9pi/4)$

Therefore,

$x=3cos((-9pi)/4)=3cos (-2pi-pi/4)=3cos(-pi/4)$

$x=3cos(pi/4)=(3sqrt2)/2$

$y=3sin((-9pi)/4)=3sin(-2pi-pi/4)=3sin(-pi/4)$

$y=3*-sqrt2/2=(-3sqrt2)/2$

The cartesian coordinates are $((3sqrt2)/2,(-3sqrt2)/2)$

What is the Cartesian form of ( 3 , (-9pi)/4 ) ( 3 , (-9pi)/4 ) ?