![]() This maximum value occurs whenever sin x = 1 or cos x = 1. The maximum value of the function is M = A + |B|. These two functions have minimum and maximum values as defined by the following formulas. This also holds for the cosine function (Figure 4 ).Įxamples of several amplitudes of the sine function.Ĭombining these figures yields the functions y = A + B sin x and also y = A + B cos x. 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. The additional factor B in the function y = B sin x allows for amplitude variation of the sine function. This also holds for the cosine function (Figure 3 ).Įxamples of several vertical shifts of the sine function. The additional term A in the function y = A + sin x allows for a vertical shift in the graph of the sine functions. Several additional terms and factors can be added to the sine and cosine functions, which modify their shapes. Multiple periods of the a) sine function and b) cosine function. The sine function and the cosine function have periods of 2π therefore, the patterns illustrated in Figure are repeated to the left and right continuously (Figure 2 ). One period of the a) sine function and b) cosine function. Next, plot these values and obtain the basic graphs of the sine and cosine function (Figure 1 ). To see how the sine and cosine functions are graphed, use a calculator, a computer, or a set of trigonometry tables to determine the values of the sine and cosine functions for a number of different degree (or radian) measures (see Table 1). ![]() Graphs: Special Trigonometric Functions.
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