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)#