5.3. Amplitude of Sinusoidal Functions http://www.ck12.org
Notice that the amplitude is 3, not 6. This corresponds to the absolute value of the maximum and minimum values
of the function. If the function had beenf(x) =− 3 ·sinx, then the whole graph would be reflected across thexaxis.
Also notice that thexaxis on the graph above is unlabeled. This is to show that amplitude is a vertical distance. The
sinusoidal axis is the neutral horizontal line that lies between the crests and the troughs (or peaks and valleys if
you prefer). For this function, the sinusoidal axis was just thexaxis, but if the whole graph were shifted up, the
sinusoidal axis would no longer be thexaxis. Instead, it would still be the horizontal line directly between the crests
and troughs.
Example A
Graph the following function by first plotting main points:f(x) =− 2 ·cosx.
Solution: The amplitude is 2, which means the maximum values will be at 2 and the minimum values will be at
-2. Normally with a basic cosine curve the points corresponding to 0,π 2 ,π,^32 π, 2 πfall above, on or below the line in
the following sequence: above, on, below, on, above. The negative sign switches above with below. The whole
graph is reflected across thex-axis.
Example B
Write a cosine equation for each of the following functions.