# In trigonometry, a general sinusoidal equation has the form y = A sin(Bt + C) +

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…