How do you find the coordinates of the terminal points corresponding to the following arc length on the unit circle: 4π/3?

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How do you find the coordinates of the terminal points corresponding to the following arc length on the unit circle: 4π/3?

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Answer 1 · 2015-05-21T12:23:45

Use the trig unit circle as proof. The coordinates of the arc's terminal point are:

$x = \frac{cos (4 π)}{3} = cos (\frac{π}{3} + π) = - cos (\frac{π}{3}) = - \frac{1}{2}$ $x = cos (4pi)/3 = cos (pi/3 + pi) = -cos (pi/3) = -1/2$ (Quadrant III)

$y = sin (\frac{4 π}{3}) = sin (\frac{π}{3} + π) = - sin (\frac{π}{3}) = \frac{- \sqrt{3}}{2}$ $y = sin ((4pi)/3) = sin (pi/3 + pi) = - sin (pi/3) = (-sqrt3)/2$ -

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How do you find the coordinates of the terminal points corresponding to the following arc length on the unit circle: 4π/3?

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