Examine graphs of the following function for different values of a, b, c
Begin by observing the parent graph y= sin x below:
A change in a changes the Altitude (the vertical height of the sin curve) such as illustrated below with a= 3. The maximum and minimum y values has been transformed to +/- 3, respectively; from the parent altitude of +/- 1 (note: when a < 0 then there is a reflection over a horizontal axis).
The Period (length of time for one complete cycle) of the function y = sin bx is 360 degrees/b. The function
y = sin 2x now completes a full cycle in 180 degrees as opposed to 360 degrees as illustrated below:
A change in b and c will create a Phase Shift (transformation to the right or left) in the sine function. In the function y = a sin (bx + c) the phase shift is -c/b. If c > 0 the shift is to the left. If c < 0, the shift is to the right. This definition applies to all of the trigonometric functions, illustrated below the function of y = sin (x + 3.14), a shift of 3.14 to the left: