How do you find the exact value of $cos((11pi)/3)$ ?

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Answer 1 · 2018-04-25T03:56:29

$1/2$

Given: $cos ((11 pi)/3)$

The cosine function has a period of $2 pi$ . This means the values of the cosine repeat every period.

See if $(11 pi)/3$ is $> 2pi$

$(2 pi)/1 = (2 pi)/1 * 3/3 = (6 pi)/3$

$(11 pi)/3 = (6 pi)/3 + (5 pi)/3 = 2pi + (5 pi)/3$

Yes $(11 pi)/3$ is $> 2pi$

The equivalent cosine value of $(11 pi)/3$ is $(5 pi)/3$

On a trigonometric circle, the $cos ((5 pi)/3) = 1/2$

Answer 2 · 2018-04-25T03:56:30

$cos( {11 pi} / 3 ) = 1 / 2$

I'm not sure why we have an entire subject dedicated to just two right triangles (30,60,90 and 45,45,90) but we sure seem to.

$\cos( {11 pi}/3 )$

$= cos({11 pi}/3 - 4pi )$

$= cos( -pi/3)$

$= cos(pi/3)$

$= cos 60^circ$

$= 1/2$

How do you find the exact value of cos((11pi)/3)cos((11pi)/3)?