Graphs of Sines/Cosines

For the general sine/cosine function $y = A \sin[B(x - C)] + D$, you can determine its properties:

• Amplitude: $|A|$
• Period: $\frac{2\pi}{B}$
• Phase Shift (horizontal): $C$
• Vertical Shift: $D$

To find the period of $y = 3\sin(\pi x - 2) + 8$, first factor out $\pi$ to get $y = 3\sin[\pi(x - \frac{2}{\pi})] + 8$. Here, $B = \pi$, so the period is $\frac{2\pi}{\pi} = 2$.