Consider the core trigonometric functions: sine and cosine.

This is apparent by reviewing the mapping diagrams along with the graphs in our initial examples for this section.

But first we review the key concepts: increasing and decreasing- and an extreme value for a function.You can use the next examples to investigate visually the effects of linear composition prior to applying the core trigonometric functions on the increasing and decreasing shape of a more general trigonometric function by considering a mapping diagram of $f$ and the graph of $f$ where $f(x) = trig(Bx+C)$ where $trig(x) = \sin(x);\ trig(x) =\cos(x);$ or $trig(x)=\tan(x)$.

You can use the next example to investigate visually the effects of other linear compositions prior to applying the core trigonometric functions on the increasing and decreasing shape of a more general trigonometric function by considering a mapping diagram of $f$ and the graph of $f$.