What are the components of the vector between the origin and the polar coordinate #(6, (5pi)/4)#?

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Answer 1 · 2018-03-19T01:02:04

#<-3sqrt(2), -3sqrt(2)>#

Given: polar coordinates #(6, (5 pi)/4)#

To convert from polar to rectangular form use:

#x = r cos theta#
#y = r sin theta#

#(6, (5 pi)/4) = (r, theta)#

The angle #(5 pi)/4# is in the third quadrant, #45^@ # past #180^@.#

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

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

#x = 6 * -sqrt(2)/2 = -3 sqrt(2)#

#y = 6 * -sqrt(2)/2 = -3 sqrt(2)#

The vector from the origin (0,0) to the point #(x, y)# is

#<-3sqrt(2), -3sqrt(2)>#