The main function of this formula is to turn the sum of multiple trigonometric functions into one function, thus solving the maximum problem.

First, the left side of the equation is the sum of two sine and cosine functions, which are increased (or decreased) by a certain multiple respectively. Look at the right side of the equation, there is a sine function, which has been increased (or decreased) by a certain multiple, and its initial phase has been changed.

Extended data:

Algebraically, the auxiliary angle formula is for several sine functions with the same frequency (

) and become a single sine function. The same frequency means

The same, so in order to facilitate the auxiliary angle formula, we only discuss it.

Special circumstances at that time. In this case, for sine functions, we only have

(Increase multiple) and

There are two quantities to discuss.