# Graphing Trigonometric Functions

*Lindsey* *Bennett* *:)*

y=sin(x) is the parent function. It repeats every 2pi radians. The range is from -1 to 1 and the amplitude is half of that distance. The period is from zero to 2pi. There is no change in shift.

y=2sin(x) represents the amplitude. In this graph the amplitude increases by two, because of the 2 in front of sin. So the amplitude in this case is -2 and 2, with a period from zero to 2pi.

y=2+sin(x) represents a vertical shift. Instead of the graph starting at the origin, the 2 added to sin causes the graph to shift up (vertically) by 2.

The function f(x)=sin(x-3) represents horizontal shift. This graph has been moved (shifted) to the left because of the -3 in the function above. The amplitude is -1 to 1.

y=sin(2x) represents the period. The period is zero to pi over 2 rather than from zero to 2pi, with an amplitude of -1 to 1.