Putting sinusoidal functions in standard form

The following are three examples of how this goes 1 f

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Unformatted text preview: ite in that form. The following are three examples of how this goes. 1. f (x) = sin(3x + 1) We factor out the 3 from the expression 3x + 1 to get 1 . f (x) = sin 3 x + 3 We want 2π = 3, so B = 2 π . Thus, B 3 f (x) = sin 2π 1 x+ 2 3 π 3 . 2 1 And we can see that A = 1, B = 3 π, C = − 3 , D = 0. 2. f (x) = sin(2 − 7x) We can factor the −7: 2 f (x) = sin −7 − + x . 7 In order to end up with B > 0 we have to do something about that −7. We can use the following identity: sin(−x) = sin(x + π ) for all x. This gives us 2 2 π = sin 7 − +...
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