Let us start to rotate the point P clockwise over the circle.
The y-coordinate of this point varies harmonically
with the angle, i.e.
.
The diagram shows how to graph the sine function by projecting the
y-coordinate of the point P horizontally.
When P returns back to its initial position after making a circle
the sine function returns back to its initial value of zero.
The Sine Function
Varying the Amplitude
Multiplying
sin x
by a positive constant A causes a vertical expantion or compression of the graph of
y = sin x.
For 0 < A < 1
there is a compression.
For A > 1 there is an expansion.
The Cosine Function
Varying the Amplitude
Multiplying
cos x
by a positive constant A causes a vertical expantion or compression of the graph of
y = cos x.
For 0 < A < 1
there is a compression.
For A > 1 there is an expansion.
Vertical Shift of Sine and Cosine Functions
Adding a constant B to
sin x
or
cos x
in the equations of the functions