How do you evaluate sine, cosine, tangent of $(4pi)/3$ without using a calculator?

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How do you evaluate sine, cosine, tangent of $(4pi)/3$ without using a calculator?

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Answer 1 · 2017-02-17T00:51:17

$- sqrt3/2 ; - 1/2 ; sqrt3$

Explanation:

Use trig table of special arcs and unit circle.
On the unit circle,
$sin ((4pi)/3) = - sin (pi/3) = - sqrt3/2$
$cos ((4pi)/3) = - cos (pi/3) = - 1/2$
$tan ((4pi)/3) = tan (pi/3) = sqrt3$

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How do you evaluate sine, cosine, tangent of $(4pi)/3$ without using a calculator?

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