AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.6 Sinusoidal Function Transformations
Notes
- $a$: vertical stretch (and reflection if negative).
- $b$: horizontal compression by $\displaystyle \frac{1}{|b|}$; changes the period.
- $c$: horizontal shift (phase shift). $d$: vertical shift.
Practice
$y=\sin(2x-\pi)$ is shifted right by:
$\displaystyle \sin\left(2\left(x-\frac{\pi}{2}\right)\right)$.
$y=\sin(x)+4$ compared with $\sin x$ is shifted:
$d=4$.
Which changes the period?
Period $\displaystyle =\frac{2\pi}{|b|}$.
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