**Symmetry of Trigonometric Functions**

Other symmetries of the trigonometric functions are related to

Consider the trigonometric functions $f(x) = A trig(Bx +C)+D $ where $trig = \sin, \cos,$ or $\tan$.

These

We explore how the symmetry of these functions, similar to the quadratic functions, can
be understood as a composition
of core functions.

In these examples we use GeoGebra to visualize symmetry with the composition for one linear core function with a core trigonometric function.

**
Example** TRIG.SYM.4:
Suppose $f$ is a cosine function with amplitude $ =A=2$
and maximum value $f(1)=3$ and period $2 \pi$. Find the composition form of the
trigonometric
function. Visualize $f$ with a mapping diagram that illustrates
the function as the composition of the four core functions
$f_{+1}∘f_{∗2}∘\cos∘f_{−1}$ with even symmetry with respect to the axis $x = 1$..

You can use this next dynamic example with GeoGebra to investigate further the symmetry of a trigonometric functions in a mapping diagram of $f$.