# 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.

When 0< a <1, the effect of multiplying sin x by $a$ is a vertical shrink.

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.

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