This screen is designed to help you to investigate functions of the type Asin(x) + Bcos(x) for different values of A and B. You should quickly notice that the functions are also simple sine or cosine curves. But what are their parameters? The functions can be rewritten as Rsin(x + a), Rsin(x - a) or Rcos(x + a), where R is a positive real number, and a is angle between 0° and 90°. To rewrite the functions in one of these forms you need to calculate the values of the parameters R and a.

By looking at the screen and trying different values of A and B, and by looking at the words on the right, you should see how to calculate R and a in different circumstances. The main purpose of this skill is to enable you to solve trigonometric equations such as 4sin(x) + 3 cos(x) = 2.
Play around. I hope you will find this applet helpful in understanding these important but tricky techniques.