How to graph SINE functions
To graph a sin function, you need to know the sine of each of the quadrant angles and reference angles. It will help you when beginning to learn how to graph sine functions. You should know the basics of general graphing by now.
Let's just graph the parent function of sine. y=sin x
You can see that the graph fluctuates from its max to its min repeatedly. The imaginary line directly in the middle of the max and min is called the midline.
The midline is traced by the dotted blue line. In the parent function y=sin x, the midline is y=0.
From the midline, we can find the amplitude of the graph. The amplitude is the distance of the max or min from the midline. In the case of the parent function the amplitude is 1. We can also find the amplitude just by looking at the function. The amplitude is the absolute value of the coefficient in front of sin.
y=[1]sin x ----> the amplitude is 1
y=[1]sin x ----> the amplitude is 1
The next thing you need to know in order to graph a sine function is its period. The period of a sine function is the distance on the x-axis of the graph before it repeats itself. The period can be found by taking the coefficient in front of x and dividing 2π by that coefficient.
y=sin [1]x ----> 2π/1 = 2π
The period of the parent function is 2π.
y=sin [1]x ----> 2π/1 = 2π
The period of the parent function is 2π.
The distance between each point on the graph is the interval. To find the intervals of a graph, you just divide the period by 4.
The initial point of y=sin x is (0,0). The initial point is where you should start drawing the graph of sine.
If a sine graph has a vertical or horizontal shift, you have to move the initial point of the parent function graph and the midline. The midline only changes with vertical shifts, but the initial point will change with either a horizontal or vertical shift.
There is a pattern in the graph of sine. The initial point of a positive sin graph will always start at its midline. Then as x increases, the function will curve to its maximum, pass through the midline, curve to its minimum, and then return the midline to end one period. For a negative sin graph, the intial point still starts at its midline, but the funtion will curve to its minimum, pass the midline, curve to its maximum, and then return to the midline. The points at the end of every interval will be at either a max, min, or the midline.