What is the polar form of #( -51,6 )#?

1 Answer
Aug 7, 2016

Polar form coordinates are #(3sqrt293,173.29^o)#

Explanation:

A rectangular coordinate #(x,y)# can be written as polar coordinate #(r,theta)#, where #x=rcostheta#, #y=rsintheta#, #theta=tan^(-1)(y/x)# and #r=sqrt(x^2+y^2)#.

As we have rectangular coordinate #(-51,6)#

#r=sqrt((-51)^2+6^2)=sqrt(2601+36)sqr2637=3sqrt293#

and #theta=tan^(-1)(-6/51)=tan^(-1)(-0.11765)=(180-6.71)^o=173.29^o#

Note - As #tantheta# is negative and while #costheta# is negative and #sintheta# is positive, we have taken #theta# in second quadrant.

Hence polar form coordinates are #(3sqrt293,173.29^o)#