Modelling with Trigonometric Functions (Edexcel A-Level Mathematics): Flashcards

$y(t) = A \sin(Bt + C) + D$ or $y(t) = A \cos(Bt + C) + D$

$A$ is the maximum value from the mean position in the model.

$T = 1/f$ relates period $T$ to frequency $f$ in trigonometry.

$C$ represents how the function is horizontally shifted.

$D$ moves the entire graph up or down vertically.

Use sine when the wave starts at the midline ($y=0$).

Use cosine for max/min at $t=0$; sine starts at zero.

$A = (max - min) / 2$ gives the amplitude value.

$D = (max + min) / 2$ calculates vertical shift.

Modelling wave motion, like in physics and engineering.