Question

solve

f(x)=sin(2arccos(1/4))

Answer 1

This is a function of x?
There is no x :o
That's strange

Answer 2

So anyway we can ummm...

Answer 3

\[\Large\rm \sin\left[2\color{orangered}{\arccos\left(\frac{1}{4}\right)}\right]\]Work from the inside out.
This inverse cosine is equal to some angle, let's call it theta.\[\Large\rm \color{orangered}{\arccos\left(\frac{1}{4}\right)=\theta}\]

Answer 4

\[\Large\rm \implies \qquad \cos \theta=\frac{1}{4}\]

Answer 5

We'll draw a triangle which satisfies this relationship.

Answer 6

Applying our Pythagorean Theorem gives us the missing side:

Answer 7

Then we can think of our problem:\[\Large\rm \sin\left[2\color{orangered}{\arccos\left(\frac{1}{4}\right)}\right]\]As:\[\Large\rm \sin\left[2\color{orangered}{\theta}\right]\]Applying our Sine Double Angle Identity:\[\Large\rm =2\sin \theta \cos \theta\]And use the triangle to finish it up.

Answer 8

I still don't see what this has to do with x.
Is it a constant function?
Or were you plugging in some value for x?