Transformations of Trigonometric Functions


Case 3:

amath
y=sin ( x + c )+d


The MATLAB file, plotsine.m illustrates the effect of adding c to x and adding d to the sine part.


Note: plotsine.m demonstrates the horizontal and vertical translations separately.

While the previous two cases changed the shape of the sine function, horizontal and vertical translations conserve the shape of the function.


c translates the graph horizontally.
If c < 0, the graph is translated to the right by |c| units.
If c > 0, the graph is translated to the left by c units.


d translates the graph vertically.
If d < 0, the graph is translated down by |d| units.
If d > 0, the graph is translated up by d units.


Some excerpts from the plots of plotsine.m to illustrate horizontal and vertical translation: c>0 d>0
For a combined vertical and horizontal translation, download plotsinehv.m: c=2 and d=3

See the next page to put the three cases together and apply our results to the cosine graph. endamath