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

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Answer 1 · 2016-08-19T01:40:33

# <-2sqrt2, -2sqrt 2> #.-

In both cartesian #(x, y) and# polar #(r, theta)# forms, the

components of the position vector #OP#, from the origin to the point

P(x,y) are # < x, y > = < r (cos theta, sin theta)> #, repectively

Here, #(r, theta)=(-4, -(7pi)/4)#. and so, the components are

#<-4 cos(-7pi/4), -4 sin(-7pi/4)>#, using cos (-a) = cos a and sin (-a)

=-sin a

#= <-4cos(7pi/4), 4 sin (7pi/4)>#

#= <-4 cos (2pi-pi/4), 4 sin (2pi-pi/4) >#

#= <-4 cos (pi/4)- 4 sin (pi/4) >#,

using #cos (2pi-a)=cos a and sin (2pi-a)=-sina#.

#= <-4/sqrt2, -4/sqrt2 >#

#= <-2sqrt2, -2sqrt 2> #.-