Question

Cos3x= square root of 3/2?

I get confused on what to do with cos3x

Answer 1

`x=(pi/18)+(2npi)/3`

`x=(11pi)/18+(2npi)/3`

Explanation:

`cos3x=sqrt3/2`

Now, were there not a `3x` and it were just an `x,` we would just look for where `cosx=sqrt3/2`.

In this case, it's not much different. Let's say `u=3x,` rewrite as

`cosu=sqrt3/2`

Okay, now for what `u` is this true?

`u=pi/6+2npi`
`u=(11pi)/6+2npi`

Let's get back in terms of `x`

`3x=pi/6+2npi`

`3x=(11pi)/6+2npi`

We need to solve for `x.` That's not really too bad, just divide both sides by three for each solution.

`x=(pi/18)+(2npi)/3`

`x=(11pi)/18+(2npi)/3`

Answer 2

`color(brown)(x = 10^@`

Explanation:

`cos 3x = sqrt3 / 2`

From the table above, `cos 30 = sqrt3 / 2`

`:. cos 3x = cos 30 = cos (3 * 10)`

`color(red)(cancel3) x = color(red)(cancel3) * 10, " or " color(brown)(x = 10^@`