What are the components of the vector between the origin and the polar coordinate #(15, (-3pi)/4)#?

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Answer 1 · 2017-11-29T18:21:24

#-(15sqrt(2))/2hati-(15sqrt(2))/2hatj#

First convert the polar coordinate in a Cartesian coordinate. This can be done using:

#x=rcos(theta)#

#y=rsin(theta)#

#x= 15cos(-(3pi)/4)=-(15sqrt(2))/2#

#y= 15sin(-(3pi)/4)=-(15sqrt(2))/2#

Cartesian coordinates:

#(-(15sqrt(2))/2 , -(15sqrt(2))/2 )#

Vector components.

#x=-(15sqrt(2))/2hati#

#y=-(15sqrt(2))/2hatj#

#:.#

#-(15sqrt(2))/2hati-(15sqrt(2))/2hatj#