How do you find the sine, cosine, and tangent of (-4pi)/3 radians?

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Answer 1 · 2018-07-04T03:29:39

$sin ((-4 pi)/3) = 1/2$
$cos ((-4 pi)/3) = sqrt(3)/2$
$tan((-4 pi)/3) = sqrt(3)/3$

Given: $(-4 pi)/3$

Add $2 pi$ to find the positive equivalent angle:

$(-4 pi)/3 + (6 pi)/3 = (2 pi)/3$

$(2 pi)/3$ is in the 2nd quadrant. The reference angle is $pi/3 = 60^@$

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$sin ((2 pi)/3) = 1/2$

$cos ((2 pi)/3) = sqrt(3)/2$

$tan ((2 pi)/3) = 1/sqrt(3) * sqrt(3)/sqrt(3) = sqrt(3)/3$