How do you convert #(5sqrt 3, −5)# to polar form?

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Answer 1 · 2016-05-21T05:43:25

Polar form of #(5sqrt3,-5)# are #(10,-pi/6)#

If Cartesian coordinates are #(x,y)# and its polar coordinates are #(r,theta)#, then

#r^2=x^2+y^2# and #tantheta=y/x#

Hence, in case of #(5sqrt3,-5)#

#r=sqrt((5sqrt3)^2+(-5)^2))=sqrt(25xx3+25#

)= #sqrt(75+225)=sqrt100=10#

and as #tanteta=-5/(5sqrt3)=-1/sqrt3#

#theta=-pi/6#

Hence polar form of #(5sqrt3,-5)# are #(10,-pi/6)#