How do you find the exact value of #(4cos330+2sin60)/3#?

1 Answer
Noah G
Nov 6, 2016

The expression can be evaluated to #sqrt(3)#.

Explanation:

Let's start by finding the values of #cos330˚# and #sin60˚#. The reference angle of #330˚# is #30˚#. By the #30-60-90# special triangle, #cos30˚ = sqrt(3)/2#. #330˚# is in quadrant #IV#, where cosine is positive, so #cos330˚ = sqrt(3)/2#.

By the #30-60-90# special triangle, #sin60˚ = sqrt(3)/2#.

We can now evaluate the expression.

#=(4(sqrt(3)/2) + 2sqrt(3)/2)/3#

#=(2sqrt(3) + sqrt(3))/3#

#=(3sqrt(3))/3#

#=sqrt(3)#

Hopefully this helps!

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