Transformations of Trigonometric Functions


amath In this site, we will explore the effect of transformations on the basic sine and cosine graphs.
We will mainly concentrate on translations and vertical/horizontal stretches and shrinks. The main analysis will comprise three sections, culminating in a final study of the graph of y=a sin ( b(x+c))+d and of y = a cos( ( b(x+c))+d .
endamath

Case 1: amath

y=a sin x


When a>1, the effect of multiplying sin x by $a$ is a vertical stretch.
a>1
When 0< a <1, the effect of multiplying sin x by $a$ is a vertical shrink.
0<a<1
When a < 0 the vertical stretch (for |a|>1) or the vertical shrink (for |a|<1) is combined with a reflection across the $x$ endamath axis. a<0
amath Recall that the a periodic function that cycles within some definite range has amplitude =(max-min)/2


The amplitude of y=a sin x is |a|.


Click here for case endamath 2:amath y = sin b x. endamath