IB Math SL Period & Amplitude of trig functions

Period

Length from one peak to the next. To find the period: 2π/|b|

Equation

a cos(bx-c)+d

Equation variables

a= amplitude b= period c= phase shift d= vertical shift

Example f(x)= 3cos(x)

f(x)= 3cos(x) a=3, b=1 |a|= |3|, amplitude: 3 2π/|b|, 2π/|1| =2π period: 2π

Example y=2cos(1/2)x

y=2cos(1/2)x a=2, b=(1/2) |a|=|2|=2 amplitude: 2 2π/|b| 2π/ |(1/2)| = 4π period: 4π

Amplitude

Height from center line to the peak To find the amplitude: |a|

Example y=-2cos(1/4)x

y=-2cos(1/4)x a= -2, b= 1/4 |a|= |-2| = 2 amplitude: 2 2π/|b| 2π/|(1/4)| = 8π period: 8π