What are the components of the vector between the origin and the polar coordinate #(2, (5pi)/4)#?

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Answer 1 · 2017-12-10T12:09:12

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

First convert the polar coordinates to Cartesian coordinates. This can be done using the following idea:

Cartesian coordinate is equal to:

#(rcostheta , rsintheta)#

#:.#

#x=rcostheta#

#y=rsintheta#

#x=2cos((5pi)/4)=-sqrt(2)#

#y=2sin((5pi)/4)=-sqrt(2)#

The component vector for #x# is #hati#

and the component vector for #y# is #hatj#

#:.#

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