The graph of the function y = sin x has the following characteristics:
Amplitude = 1
Period = 2pi
Phase shift = 0
Axis of Oscillation y = 0
The standard form of the equation of the sine function is y = A sin (B(x - C)) + D
A is the amplitude.
B can be used to find the period (period = 2pi/B).
C is the phase shift.
D is the axis of oscillation.
Steps for graphing the sine function:
Use A, B, C, D to identify the amplitude, period, phase shift and axis of oscillation.
Find the "starting point" of the graph using the phase shift for x and the axis of oscillation for y.
Add the period to the phase shift to find the "end point".
Find the midpoint by averaging the "start" and "end".
Find the quarter point by averaging the "start" with the midpoint.
Find the three-quarter point by averaging the "end" with the midpoint.
Check the sign of A and B to see if you should start with a peak or a trough.
Check the size of A to see how high your peak should be above your axis of oscillation and how low your trough should be below the axis of oscillation.
Graph the function!