What are the components of the vector between the origin and the polar coordinate $(- 1, \frac{4 π}{3})$ $(-1, (4pi)/3)$ ?

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Answer 1 · 2017-11-19T11:03:52

$\frac{1}{2} ˆ i + \frac{\sqrt{3}}{2} ˆ j$ $1/2hati+sqrt(3)/2hatj$

First we need to convert the polar coordinates into Cartesian coordinates. We can do this using:

$x = r cos θ$ $x= rcostheta$
$y = r sin θ$ $y= rsintheta$

$x = - 1 cos (\frac{4 π}{3}) = \frac{1}{2}$ $x= -1cos((4pi)/3)=1/2$

$y = - 1 sin (\frac{4 π}{3}) = \frac{\sqrt{3}}{2}$ $y= -1sin((4pi)/3)=sqrt(3)/2$

Cartesian coordinates:

$(\frac{1}{2}, \frac{\sqrt{3}}{2})$ $( 1/2 , sqrt(3)/2 )$

$\frac{1}{2} ˆ i + \frac{\sqrt{3}}{2} ˆ j$ $1/2hati+sqrt(3)/2hatj$

What are the components of the vector between the origin and the polar coordinate (-1, (4pi)/3)(−1,4π3)(-1, (4pi)/3)?