Amplitude:
If you look at the graphs of the Sine and Cosine functions, you see that they always take values between -1 and 1. Amplitude is defined as the maximum difference between the value of a periodic function and its mean. In the case of both y=sin(x) and y=cos(x), their means are 0. Thus the amplitude of both these functions is 1.
The following graph shows the Sine Curve multiplied by the variable, a. If you change a to a different number, the graph redraws with a new amplitude. To change a, highlight the value of a with the mouse and then type a new number. The dashed black line is the Sine Curve with an amplitude of 1.
Angular Frequency:
The Angular Frequency is the number of periods that a function runs through between 0 and 2*Pi. In the following graph, where b=1, there is one period. If we change b to 2, there will be two periods. Try changing the value of b several times and watch the graph update itself.
Horizontal Shift:
We can shift a trigonometric graph to the right or to the left by adding a value to or subtracting a value from the variable. For example sin(x+1) will be the Sine Curve shifted right by a value of 1. In the following graph, try changing the value of h from 0 to 1. Try other numbers, including some negative numbers, and also try Pi and 2*Pi.
Vertical Shift:
Changing the value of v in the following graph shifts the Sine Curve up or down by that amount. Change v from 0 to 1, then try -1. Remember that to change the sign of a number, highlight the number and press the "-" key.
Experimenting
As you change the values of a, b, h, and v in the following notebook, MathView automatically redraws the graph. The original curve, f(x)=sin(x), appears as a dotted black line.
Source:Waterloo Maple Inc., Canada (Modified by LuaSK)