How to Graph Sine Waves
- 1). Examine the sine function, of the form f(x) = asin(bx + c) + d, to determine its amplitude and phase shift; its "a" and "b" values.
- 2). Graph the amplitude by plotting the maximum and minimum points of the sine graph equal to its value. The positive value of "a" is the maximum value of f(x) and the negative value is the minimum value of f(x). For example, for f(x) = asin(x), 0 <= x <= 2Pi, the maximum point is at x = Pi/2 and the minimum point is at x = 3Pi/2. The y-value is determined by the size of "a."
- 3). Determine the period of the graph by using the equation: Period = (2PI / b). As "b" increases the period increases as the graph is "stretched." As "b" increases the graph is "compressed" and the period decreases. The period equation determines where the graph touches the x-axis.
- 4). Shift the graph horizontally depending on the value of "c." If "c" is a positive value then the graph is shifted "c" units to the left. If it is negative, then the graph is shifted "c" units to the right.
- 5). Shift the graph vertically depending on the value of "d." If "d" is positive then the graph is shifted "d" units up. If it is negative then the graph is shifted "d" units down.