y = a sin x + b cos x


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.


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.


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.

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