y = a sin x + b cos x

Introduction

The figure shows the idea of constructing the function; y = a sin x + b cos x

The angle OAP is always 90 degrees. When the figure OAP rotates arround the origin, the y-coordinate of point P represents the function.

Applet

The applet shows the graph of
y = a sin x + b cos x

The initial value of a and b are 1 and 0.5 respectively.

To draw the graph, press "Draw" button.

Exploration

Using the applet, you can observe the graph of y=a sin x + b cos x is a simple sine curve with the same period in any cases. However, the amplitude and phase shift are different.

Find A and p that satisfies the equation
Find the general method to determine A and p using the value of a and b.

The idea was originally presented by SASAKI Shuichi at Iwate high school in 1989.