What are the components of the vector between the origin and the polar coordinate $(10, \frac{7 π}{6})$ $(10, (7pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate $(10, \frac{7 π}{6})$ $(10, (7pi)/6)$ ?

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Answer 1 · 2016-02-19T05:30:13

Components are $- 5 \sqrt{3}$ $-5sqrt3$ along $x$ $x$ axis and $- 5$ $-5$ along $y$ $y$ axis.

Explanation:

Components of a vector between the origin and the polar coordinate $(r, θ)$ $(r,theta)$ can be written as $(r cos θ, r sin θ)$ $(rcostheta, rsintheta)$ , where $r cos θ$ $rcostheta$ is the component along $x$ $x$ axis and $r sin θ$ $rsintheta$ is the component along $y$ $y$ axis.

Hence, components of a vector between the origin and the polar coordinate $(10, \frac{7 π}{6})$ $(10,(7pi)/6)$ are

$10 cos (7 \frac{π}{6})$ $10cos(7pi/6)$ or $10 \cdot (- \frac{cos π}{6})$ $10*(-cospi/6)$ i.e. $10 \cdot - \frac{\sqrt{3}}{2}$ $10*-sqrt3/2$

or $- 5 \sqrt{3}$ $-5sqrt3$ along $x$ $x$ axis

$10 \frac{sin (7 π)}{6}$ $10sin(7pi)/6$ or $10 \cdot (- \frac{sin π}{6})$ $10*(-sinpi/6)$ i.e. $10 \cdot - \frac{1}{2}$ $10*-1/2$

or $- 5$ $-5$ along $y$ $y$ axis

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What are the components of the vector between the origin and the polar coordinate $(10, \frac{7 π}{6})$ $(10, (7pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate (10,7π6)(10, (7pi)/6)?

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What are the components of the vector between the origin and the polar coordinate $(10, \frac{7 π}{6})$ $(10, (7pi)/6)$ ?