Chapter 1 | Functions and Graphs
71
Figure 1.34 The six trigonometric functions are periodic.
Just as with algebraic functions, we can apply transformations to trigonometric functions. In particular, consider the following function: (1.10) f ( x ) = A sin ⎛ ⎝ B ( x − α ) ⎞ ⎠ + C . In Figure 1.35 , the constant α causes a horizontal or phase shift. The factor B changes the period. This transformed sine function will have a period 2 π / | B | . The factor A results in a vertical stretch by a factor of | A |. We say | A | is the “amplitude of f . ” The constant C causes a vertical shift.
Figure 1.35 A graph of a general sine function.
Notice in Figure 1.34 that the graph of y =cos x is the graph of y = sin x shifted to the left π /2 units. Therefore, we
Made with FlippingBook - professional solution for displaying marketing and sales documents online