# Graphs of Trigonometric Functions Asin(x) + Bcos(x)

Examine graphs of the trigonometric functions Asin(x) + Bcos(x) for different values or A and B. See how they relate to transformations of single sine or cosine functions, and how these can help to solve more complicated trigonometric equations.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5 AS and A2 Level Core Mathematics, Trigonometry

TweetInstructions below See also: Trigonometric Transformations Trigonometric Equations Trigonometric Functions

## How to Use this Applet

This screen is designed to help you to investigate functions of the type *A*sin(*x*)
+ *B*cos(*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 *R*sin(*x* + *a*), *R*sin(*x* - *a*) or *R*cos(*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.