Stretching and Compressing Graphs of Trigonometric Functions

Here we will talk about graphing functions of the form `y=msin(kx)`, `y=mcos(kx)`, `y=mtan(kx)`, `y=mcot(kx)`.

Example. Draw graph of the function `y=-3cos(2x)`.transformation of trigonometric functions

Let's draw one half-wave of the graph `y=cos(x)`. We first compress it with coeffcient 2 to y-axis and obtain graph of the function. Now, we stretch graph of the function `y=cos(2x)` with coeffcient 3 from x-axis and reflect result about x-axis. In result we will obtain one half wave of the function `y=-3cos(2x)`. On a figure ileft graph is graph of the half-wave and right graph is all graph.