What are the components of the vector between the origin and the polar coordinate $(2, \frac{5 π}{6})$ $(2, (5pi)/6)$ ?

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Answer 1 · 2016-11-18T03:39:49

$2 < cos (\frac{5}{6} π), sin (\frac{5}{6} π) > = 2 (- \frac{\sqrt{3}}{2}, \frac{1}{2})$ $2 < cos(5/6pi), sin(5/6pi)> =2(-sqrt3/2, 1/2)$

$= < - \sqrt{3}, 1 >$ $= < -sqrt3, 1 >$

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

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

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

Observe that the unit vector in the direction $O P$ $OP$ is

$< cos θ, sin θ >$ $< cos theta, sin theta >$ .

Here $O P = 2 < cos (\frac{5}{6} π), sin (\frac{5}{6} π) >$ $OP = 2< cos (5/6pi), sin (5/6pi)>$

$= 2 < cos (π - \frac{π}{6}), sin (π - \frac{π}{6}) >$ $= 2 < cos(pi-pi/6), sin (pi-pi/6)>$

$= 2 < - cos (\frac{π}{6}), sin (\frac{π}{6}) >$ $=2 <-cos(pi/6), sin(pi/6)>$

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

$= < - \sqrt{3}, 1 >$ $=<-sqrt3, 1>$ .

What are the components of the vector between the origin and the polar coordinate (2,5π6)(2, (5pi)/6)?