What are the components of the vector between the origin and the polar coordinate #(2, (5pi)/6)#?

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Answer 1 · 2016-11-18T03:39:49

#2 < cos(5/6pi), sin(5/6pi)> =2(-sqrt3/2, 1/2)#

#= < -sqrt3, 1 >#

The position vector #OP#, from the pole ( origin ) O to the point

#P(r, theta) # is #r< cos theta, sin theta># in polar form and

#< x, y>#, in cartesian form.

Observe that the unit vector in the direction #OP# is

# < cos theta, sin theta > #.

Here #OP = 2< cos (5/6pi), sin (5/6pi)>#

# = 2 < cos(pi-pi/6), sin (pi-pi/6)>#

# =2 <-cos(pi/6), sin(pi/6)>#

#=2<-sqrt3/2, 1/2>

#=<-sqrt3, 1>#.