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.

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.

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:

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