Question

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

Answer 1

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!