How do you find the exact value of $cos (5pi)/6$ ?

Question

24278 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-22T04:36:09

$(cos(5pi))/6=-1/6$

but $cos((5pi)/6)=-sqrt3/2$

Well cosine of odd multiples of $pI$ is always $-1$ hence $cos(5pi)=-1$ and

$(cos(5pi))/6=-1/6$

However, if you mean $cos((5pi)/6)$ ,

it can be found by using identity $cos(pi-x)=-cosx$

and $cos((5pi)/6)$

= $cos(pi-pi/6)$

= $-cos(pi/6)$

= $-sqrt3/2$

Answer 2 · 2017-07-22T05:01:39

Here is the answer in which you can solve it more easy; but you will need to know the unit circle.

There are two ways that can be done but they can be done faster if you memorize the unit circle.

Convert $(5pi)/6$ to angle degrees by using the equation:

$rad*(180/pi) = degrees$

$(5pi)/6*180/pi = 150^@$

And we can figure out that the reference angle for $150^@$ is $30^@$ .

If you memorize the unit circle this step can pass much faster!

$cos30^@ = sqrt(3)/2$

Since $150^@$ is in the 2nd quadrant, we know cosine is negative.

$cos30^@ = cos( (5pi)/6) = -sqrt(3)/2$

How do you find the exact value of cos (5pi)/6cos (5pi)/6?