How can I calculate the maximum value of the compound angle formulae Rsin(x+a) and Rcos(x+a)?

Often, the compound angle formulae can seem quite offputting, especially since exam pressures can mean the random "R" at the front of an angle addition formulae appears confusing. However, finding the maximum (or minimum) for these formulae is relatively straightforward. If we let x+a=t, then we have Rsin(t) and Rcos(t). Thinking about the graphs for sine and cosine, we know that the maximum value that we can get on the y-axis is 1, so the maximum of sin(t) and cos(t) will be 1 (and the minimum will be -1). So, to get the maximum and minimum values, all we have to do is multiply by R. Hence, the maximum value of Rsin(x+a) will be R, and similarly for Rcos(x+a) the maximum value will be R.