What are the components of the vector between the origin and the polar coordinate $(8, \frac{π}{6})$ $(8, (pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate $(8, \frac{π}{6})$ $(8, (pi)/6)$ ?

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Answer 1 · 2016-02-10T16:01:40

Component of the vector along $x$ $x$ axis is $4 \sqrt{3}$ $4sqrt3$ and component along $y$ $y$ axis is $4$ $4$ .

Explanation:

Components of a vector between the origin and the polar coordinate $(r, θ)$ $(r, theta)$ are $r cos θ$ $r cos theta$ (along $x$ $x$ axis)
and $r sin θ$ $r sin theta$ (along $y$ $y$ axis).

Accordingly components are $8 \frac{cos π}{6}$ $8 cos pi/6$ (along $x$ $x$ axis)
and $8 \frac{sin π}{6}$ $8 sin pi/6$ (along $y$ $y$ axis).

As $\frac{cos π}{6} = \frac{\sqrt{3}}{2}$ $cos pi/6 = sqrt 3/2$ and $\frac{sin π}{6} = \frac{1}{2}$ $sin pi/6 = 1/2$ ,

component of the vector along $x$ $x$ axis is $8 \cdot \frac{\sqrt{3}}{2}$ $8* sqrt 3/2$ or $4 \sqrt{3}$ $4sqrt3$ and component along $y$ $y$ axis is $8 \cdot \frac{1}{2}$ $8* 1/2$ or $4$ $4$ .

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What are the components of the vector between the origin and the polar coordinate $(8, \frac{π}{6})$ $(8, (pi)/6)$ ?

1 Answer

Explanation:

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What are the components of the vector between the origin and the polar coordinate $(8, \frac{π}{6})$ $(8, (pi)/6)$ ?