11-06: Sinusoidal Functions

Periodic Function: a function that repeats itself at regular intervals

Period: one cycle of the graph

Trough: the minimum point

Peak: the maximum point

Equation of the axis: the mean between the peak and trough (halfway)

Amplitude: the distance from the axis to the peak or trough

Sin Functions

Parent Function: y = sinx

^^axis → max → axis → min → axis^^

Cos Functions

Parent function: y = cosx

^^max → axis → min → axis → max^^

Transformations

Sin and Cos Functions Are Transformed Into…

Sin:

g(x) = asin(k(x-d)) + c

Cos:

g(x) = acos(k(x-d)) + c

Find:

• a: amplitude → a = (max - min)/2
• c: equation of the axis → c = (max + min)/2
• k: number of cycles (period) → k = 360/Period
• d: horizontal (phase) shift → if needed, it is the amount that has been shifted over
• Find max: c + |a| = max
• Find min: c - |a| = min
• Increments of the graph: P/4