What are the components of the vector between the origin and the polar coordinate $(-1, (pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate $(-1, (pi)/6)$ ?

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Answer 1 · 2016-01-05T02:34:33

The minus 1 flips the point $180^o$ from Quadrant I to Quadrant III ...

Explanation:

So, $(-1, pi/6) = (1,(7pi)/6)$

Using a Unit Circle (since $r=1$ ), $x=-sqrt3/2$ and $y=-1/2$

Therefore, the endpoint of the vector is $(-sqrt3/2, -1/2)$

Finally, the components of a vector starting at the origin and ending at $(-sqrt3/2, -1/2)$ is $a=-sqrt3/2$ and $b=-1/2$ and using the unit vectors $i and j$ :

$-sqrt3/2i-1/2j$

or it can just be written as $<-sqrt3/2,-1/2>$

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What are the components of the vector between the origin and the polar coordinate $(-1, (pi)/6)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate (-1, (pi)/6)(-1, (pi)/6)?

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What are the components of the vector between the origin and the polar coordinate $(-1, (pi)/6)$ ?