What are the components of the vector between the origin and the polar coordinate $(-1, (7pi)/6)$ ?

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Answer 1 · 2016-01-13T12:36:30

$< sqrt(3)/2, 1/2 >$

$theta = (7pi)/6$ would be in Quadrant III
but the negative sign on the radius $(r=-1)$ shifts it back through the origin into Quadrant I

Polar coordinate $(-1,(7pi)/6)$
is therefore equivalent to $(1,pi/6)$
which is a standard angle as in the image below:
enter image source here

What are the components of the vector between the origin and the polar coordinate (-1, (7pi)/6)(-1, (7pi)/6)?