Sine and Cosine GraphsA series of free High School Trigonometry Video Lessons from Brightstorm.
Graphs of the Sine and Cosine Functions Sine and cosine are periodic functions, which means that sine and cosine graphs repeat themselves in patterns. You can graph sine and cosine functions by understanding their period and amplitude. Sine and cosine graphs are related to the graph of the tangent function, though the graphs look very different.
Transforming the Graphs of Sine and Cosine The coefficients A and B in y=Asin(Bx) or y=Acos(Bx) each have a different effect on the graph. If A and B are 1, both graphs have an amplitude of 1 and a period of 2pi. Forsine and cosine transformations, when A is larger than 1, the amplitude increases and is equal to the value of A; if A is negative, the graph reflects over the x-axis. When B is greater than 1, the period decreases; use the formula 2pi/B to find the period.
More Transformations of Sine and Cosine In the equation y=Asin(B(x-h)), A modifies the amplitude and B modifies the period; see sine and cosine transformations. The constant h does not change the amplitude or period (the shape) of the graph. It shifts the graph left (if h is negative) or right (if h is positive) and in the amount equal to h. The amount of horizontal shift is called the phase shift, which equals h.
Find an Equation for the Sine or Cosine Wave When finding the equation for a trig function, try to identify if it is a sine or cosine graph. To find the equation of sine waves given the graph, find the amplitude which is half the distance between the maximum and minimum. Next, find the period of the function which is the horizontal distance for the function to repeat. If the period is more than 2pi, B is a fraction; use the formula period=2pi/B to find the exact value. Last, find any phase shift, h.
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