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)#