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!

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
1674 views around the world
You can reuse this answer
Creative Commons License