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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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 · 2016-09-05T18:42:34

$((-sqrt3),(-1))$

Explanation:

To convert from $color(blue)"polar to cartesian coordinates"$

That is $(r,theta)to(x,y)$

$color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))$

here r = 2 and $theta=-(5pi)/6$

$rArrx=2cos(-(5pi)/6)" and " y=2sin(-(5pi)/6)$

$color(orange)"Reminder"$

$color(red)(|bar(ul(color(white)(a/a)color(black)(cos(-(5pi)/6)=-cos(pi/6))color(white)(a/a)|)))$

and $color(red)(|bar(ul(color(white)(a/a)color(black)(sin(-(5pi)/6)=-sin(pi/6))color(white)(a/a)|)))$

$rArrx=-2cos(pi/6)=-2xxsqrt3/2=-sqrt3$

and $y=-2sin(pi/6)=-2xx1/2=-1$

Thus the components of the vector are $((-sqrt3),(-1))$

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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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Explanation:

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

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