4.2 Amplitude, Reflection, & Period for Sine and Cosine
y = k + Asin(Bx + C)
y = k + Acos(Bx + C)
Amplitude - If A > 0, then the graphs of y = Asinx and y = Acosx will have
amplitude A and range [-A, A]. Amplitude is |A|.
The graphs will be reflected about the x-axis if A < 0.
If A is any real number and B > 0, then the graphs of y = AsinBx and y = AcosBx will
have period = 2π
B
ex. 1 y = 2sinx for
amp =
period =
ex. 2
amp =
period =
y = -½cosx sketch 1 complete cycle
ex. 3
amp =
period =
y = sin ½x
sketch 1 complete cycle
ex. 4
amp =
period =
y = 5sin 3x
sketch 1 complete cycle
ex. 5
amp =
period =
y = cos πx
for -2≤x≤4
ex. 6
amp =
period =
y = 2cos (-3x)
for 0≤x≤2π
ex. 7
amp =
period =
y = sin (-½3x)
sketch 1 cycle
ex. 8
amp =
period =
y = -3sin 2x
for -2π≤x≤2π