AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.5 Sinusoidal Functions
Notes
A sinusoidal function has the shape of a sine graph: $f(x)=a\sin(b(x-c))+d$.
- Amplitude $|a|$; midline $y=d$; period $\displaystyle \frac{2\pi}{|b|}$; phase shift $c$.
Practice
Amplitude of $y=-3\sin(2x)+1$:
$|a|$.
Period of $y=\cos(4x)$:
$\displaystyle \frac{2\pi}{4}$.
Midline of $y=2\sin x-5$:
The vertical shift $d$.
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