How would you find the exact trigonometric ratio for an angle whose radian measure is $(4pi)/3$ ?

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Answer 1 · 2015-07-05T20:46:11

An angle of $(4pi)/3$ is in Quadrant 3 with a reference angle of $pi/3$
$sin((4pi)/3) = -sqrt(3)/2$
$cos((4pi)/3) = -1/2$
$tan((4pi)/3) = sqrt(3)$

See diagram below:
enter image source here

Note that $pi/3$ is one of the standard trigonometric angles.

How would you find the exact trigonometric ratio for an angle whose radian measure is (4pi)/3(4pi)/3?