Maximum and minimum values on harmonic form.

ok, so lets consider $rsin(\theta + \alpha)$, what is the maximum y value that $y=\sin x$ gives? You can see by considering the graph of $y=\sin x$ that the highest y value that it reaches for any given x is y=1. Then consider what value of x this maximum occurs at? i.e. where does $\sin x = 1$, when x is an acute angle (i.e. $0 \leq x \leq 90$).Then note that we're working with $rsin(\theta + \alpha)$ so the maximum point occurs when $sin(\theta + \alpha)=1$, which is when $(\theta + \alpha)=90^{\circ}$. So you must find an appropriate value of theta for which sin is at it's maximum point i.e. 1, once you found that you realise that the maximum value of the whole expression $rsin(\theta + \alpha)$ when $sin(\theta + \alpha)=1$ must be just $r$.
For minima you must follow the same steps as above but in this case you should consider where the sin graph is at it's lowest point, which is -1. Therefore the minimum value of the expression we started with, $rsin(\theta + \alpha)$ is just $-r$.
For other trig functions you do the same. Find the minimum/maximum value of the trig graph and what x-value or angles that it occurs at, then make sure that the angle of the trig function is set to result in the whole expression being equal to it's maximum value.
Hope that helped, if there's anything you don't understand give me a shout.