Figure 3 Examples of several vertical shifts of the sine function. The additional factor B in the function y = B sin x allows for amplitude variation of the sine function. The amplitude, B , is the maximum deviation from the x‐axis—that is, one half the difference between the maximum and minimum values of the graph.

Provided by Tutoring Services 2 How to Graph Trigonometric Functions Created September 2013 Graphing Sine and Cosine Functions. Sine and Cosine. Sine and Cosine.

This also holds for the cosine function (Figure 4 ). Download Free Software Meyer Pecan Cracker Manual High School. Figure 4 Examples of several amplitudes of the sine function. Combining these figures yields the functions y = A + B sin x and also y = A + B cos x. Wedding March Classical Guitar Pdf Hal. These two functions have minimum and maximum values as defined by the following formulas. The maximum value of the function is M = A + B .

This maximum value occurs whenever sin x = 1 or cos x = 1. The minimum value of the function is m = A ‐ B . This minimum occurs whenever sin x = −1 or cos x = −1.

Example 1: Graph the function y = 1 + 2 sin x. What are the maximum and minimum values of the function? Release Some Tension Swv Rare more.

The maximum value is 1 + 2 = 3. The minimum value is 1 −2 = −1 (Figure 5 ). The additional term D in the function y = sin ( x + D) allows for a phase shift (moving the graph to the left or right) in the graph of the sine functions. (This also holds for the cosine function.) The phase shift is D . This is a positive number. It does not matter whether the shift is to the left (if D is positive) or to the right (if D is negative).

The sine function is odd, and the cosine function is even. The cosine function looks exactly like the sine function, except that it is shifted π/2 units to the left (Figure 8 ). In other words.