What are the components of the vector between the origin and the polar coordinate #(6, pi/3)#?

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Answer 1 · 2018-03-25T17:16:38

#(3,3sqrt(3))#

The coordinates of the vector are the rectangular coordinates.

So let's convert the polar coordinates to rectangular form using the formula:

#(r, theta)->(x,y)#

#x=rcostheta#
#y=rsintheta#

#x=(6)cos(pi/3)=6(1/2)=3#

#y=(6)sin(pi/3)=6(sqrt(3)/2)=3sqrt(3)#

So the vector components are #(3, 3sqrt(3))#