C3: maximum and minimum values

I am really struggling with these types of questions where they ask you to work out what the maximum value of a trig function is and at what x-value it occurs etc.

Would anyone be able to explain the theory behind this so I can understand these ques and work them out properly?

Eg:

Sin3X= 3sinx - 4sin^3x

Determine the greatest posible value of:

9 sin(10/3a) - 12 sin^3(10/3a)

Apologies as i dont know how to use latex.

If you mean the $R\sin(x- \theta)$ and $R\cos(x- \theta)$

Then the maximum value or minimum value is just 1 x R of the function. It is derived from the original $\sin \theta$ and $\cos \theta$ graphs

The answer to the above question is 9. I have no idea how to do these questions. !!!!!!!!!!!!!!!!!!!!!