Putting sinusoidal functions in standard form

# Putting sinusoidal functions in standard form - How do I...

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How do I get sinusoidal functions into the “standard” form? When confronted with a sinusoidal function, it is helpful to have it (or get it into) the form f ( x ) = A sin p 2 π B ( x - C ) P + D since we are able to read off the parameters A, B, C, and D; these parameters determine the shape and location of the graph of function. We are always able to put sinusoidal functions into this form with A > 0 , and B > 0 . Frequently, sinusoidal functions do not appear to us in this form, but we can rewrite in that form. The following are three examples of how this goes. 1. f ( x ) = sin(3 x + 1) We factor out the 3 from the expression 3 x + 1 to get f ( x ) = sin p 3 p x + 1 3 PP . We want 2 π B = 3 , so B = 2 3 π . Thus, f ( x ) = sin ± 2 π 2 3 π p x + 1 3 P ² . And we can see that A = 1 ,B = 2 3 π,C = - 1 3 ,D = 0 . 2. f ( x ) = sin(2 - 7 x ) We can factor the
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