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…