What are the components of the vector between the origin and the polar coordinate #(-7, (-pi)/4)#?

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Answer 1 · 2017-11-14T09:34:57

#(-7sqrt(2))/2 hati +(7sqrt(2))/2 hatj#

This is much easier to solve if you convert the polar coordinates into Cartesian coordinates first. This can be achieved using:

#x=rcostheta#

#y=rsintheta#

#x=-7cos((-pi)/4)=(-7sqrt(2))/2#

#y=-7sin((-pi)/4)=(7sqrt(2))/2#

Cartesian coordinates:

#((-7sqrt(2))/2 , (7sqrt(2))/2 )#