How do you simplify $cos 2(pi/3)$ ?

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Answer 1 · 2018-03-19T05:59:27

The simplified answer is $-1/2$ .

$color(white)=cos2(pi/3)$

$=cos(2*pi/3)$

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

You can use a unit circle to help you out:

enter image source here

We can see that $cos((2pi)/3)$ is just $-1/2$ .

Answer 2 · 2018-03-19T06:03:59

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

let $theta = pi/3$

$cos 2 theta = cos 2(pi/3) = cos^2 (pi/3) - sin^(pi/3) color(white)(aaa)$ as $cos (2 theta) = cos^2 theta - sin^2 theta$ identity.

enter image source here
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$=> (sqrt3/2)^2 - (1/2)^2 = 3 / 4 - 1/4 = 1/2$

How do you simplify cos 2(pi/3)cos 2(pi/3)?