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 formf(x) =Asinp2πB(x-C)P+Dsince we are able to read off the parameters A, B, C, and D; these parameters determinethe shape and location of the graph of function. We are always able to put sinusoidalfunctions into this form withA >0, andB >0.Frequently, sinusoidal functions do not appear to us in this form, but we can rewrite inthat form. The following are three examples of how this goes.1.f(x) = sin(3x+ 1)We factor out the 3 from the expression3x+ 1to getf(x) = sinp3px+13PP.We want2πB= 3, soB=23π. Thus,f(x) = sin±2π23πpx+13P².And we can see thatA= 1,B=23π,C=-13,D= 0.2.f(x) = sin(2-7x)We can factor the
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Sin, English-language films, Graph of a function, Sine wave, Identity element