Up until now, this text has dealt with trigonometric functions of single angles, and basic trigonometric identities. In the following lessons, we'll discuss trigonometric functions of multiple angles, and identities of multiple trigonometric functions.
When you have a single function and a single angle, calculations are easy. Even when the angle is a variable, a graph quite easily illustrates how the functions of the variable angle will behave. Therefore, as we learn formulas for calculating values of functions of angle sums, products, and sums and products of different functions, you may wonder why such formulas are necessary or useful. But the formulas (identities, actually, because they're true for all angles) we'll learn over the following sections help simplify complicated double-variable trigonometric equations and thereby allow us to calculate those double-variable equations through the more simple techniques we've already seen. With this knowledge, the field of trigonometry will become so wide open, you'll have to wear shades.