How do you find the polar coordinates given the rectangular coordinates (2,-2)?

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Answer 1 · 2016-12-23T15:46:59

The answer is #=(2sqrt2, -pi/4)#

To convert from rectangular coordinates #(x,y)# to polar coordinates #(r.theta)#, we use the following equations

#x=rcostheta#

#y=rsintheta#

and #r=sqrt(x^2+y^2)#

Here, #(x,y)# is #(2,-2)#

#r=sqrt(4+4)0sqrt8=2sqrt2#

#costheta=2/(2sqrt2)=sqrt2/2#

#sintheta=-2/(2sqrt2)=-sqrt2/2#

For these values of #costheta# and #sintheta#, we are in quadrant IV

#:.theta=-pi/4#

The polar coordinates are #(2sqrt2, -pi/4)#