In trigonometry, a general sinusoidal equation has the form y = A sin( Bt + C ) + D [or y = A cos( Bt + C ) + D ].

In trigonometry, a general sinusoidal equation has the form y = A sin(Bt + C) + D [or y = A cos(Bt + C) + D]. We can develop a general solution for this equation using inverse operations and the inverse trigonometric functions. Work through the guided solution that follows.

               For y = A sin(Bt + C) + D:

               i)    subtract D from both sides:                                                          ii)    divide both sides by A:              

             iii)    apply sin-1 to both sides and simplify:                                      iv)    subtract C from both sides:

               v)    divide both sides by B:                                                                iv)    general solution: 

y = A sin(Bt + C) + D i) y − D = A sin(Bt + C) ii) y−Dsin(Bt + C)A iii) iv) v) −1 sin −1 sin sin−1 y−DA y−DA y−DA = Bt + C − C = Bt −C B 1vi) t = sin−1B =t...