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

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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#