### Trigonometric Functions by Dylan Joyner

Parent Table for all following graphs

The parent table for all of the following sin graphs is shown first. The first graph you see is the graph of f(x)=sin(x) and this graph will always start at zero without a vertical shift. The amplitude is 1, the period is 2 times pi, the phase shift is zero, and the vertical shift is also zero, it shows the five points of each ordered pair on the table. The range of a said sin function would be -1 is less than or equal to y which is less than or equal to 1.

The four following graphs below will show the individual effects of the amplitude, period, phase shift, and vertical shift in that order.

The description of how the amplitude changes the graph is that the amplitude is the absolute value of the range because it measures the distance over the y axis the line travels for each period. The effect of the period is that it controls the rate at which the graph moves. The effect of the horizontal shift is that it changes where the graph starts along the x-axis. A vertical shift changes where the graph starts along the y-axis.

This is an unchanged cos graph

This shows the effect of the change in period of 2

This shows the changes in horizontal shift by 2

This shows change in amplitude of 2

This shows the change of vertical shift of 2

The vertical shift of 2

The amplitude of 2

This shows the period of 2

The horizontal shift of 2

The change in period of 2.

The horizontal shift change of 2.

The change of the amplitude of 2.

The vertical shift of 2.

Period of 2

Horizontal shift of 2

Amplitude shift of 2

This shows vertical shift of 2

Amplitude of 2

The vertical change of 2

The period change of 2

The horizontal change of 2

The graph above shows the changes that period, amplitude, vertical, and horizontal shifts cause in the cosecant graph.