# Graphing Trigonometric Functions Project

### By: Catherine Potter

Sin Functions:

f(x)=sin(x) is the parent graph

amplitude=2

period=1

range=-2 is less than or equal to y which is less than or equal to 2

phase shift=0

vertical shift=0

f(x)=2 sin(x)

amplitude= 2

period= 1

range=-2 is less than or equal to y which is less than or equal to 2

period shift=0

vertical shift=0

f(x)=2 sin(2x)

amplitude=2

period=2

range-2 is less than or equal to y which is less than or equal to 2

period shift=0

vertical shift=0

f(x)=2sin(2x-4)

amplitude=2

period=2

range=-2 is less than or equal to y which is less than or equal to 2

period shift=0

vertical shift=3

f(x)=5+2sin(2x-4)

amplitude=6.514

period=2

range=3 is less than or equal to y which is less than or equal to 7

period shift=2

vertical shift=6.514

The general characteristics of of each function include the amplitude, shape, period, range, vertical shift, horizontal shift.  The amplitude is the height of the wave of the function. The period is the moving of the wave in which repeats in the pattern of y values on regular intervals. The horizontal (phase) shift is the movement left or right in wave.  The range is is how high and low the wave goes, and is usually shown using inequality signs. The vertical shift is the movement up or down in the wave. The shape of the wave is determined by the  numbers in the function.