What is the polar form of #(4,-2)#?

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Answer 1 · 2016-01-21T22:55:05

#P_("(4,-2)")-> (r,theta)-> (2sqrt(5)color(white)(.),333.435^o) " polar"#

Tony B

#color(blue)("Length from origin to point (4,-2)"->r)#

#color(blue)(r=)sqrt(4^2+(-2)^2) =sqrt(20)=sqrt(2^2xx5)=color(blue)(2sqrt(5))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Angular measure")#

#theta =360-tan^(-1)(2/4)#

#color(blue)(theta~~ 333.435^o)# to 3 decimal places

Or in radians #theta~~5.82 " radians"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So #P_("(4,-2)")-> (r,theta)-> (2sqrt(5)color(white)(.),333.435^o) " polar"#