Graphing Sine and Cosine

Precalculus Honors

The General Form

The equations for sine and cosine transformations are:

\[y = a \sin(b(x - h)) + k\] \[y = a \cos(b(x - h)) + k\]

Key Components

• Amplitude: \(|a|\) (Vertical stretch/compression)
• Period: \(\frac{2\pi}{b}\)
• Phase Shift: \(h\) (Horizontal shift)
• Midline: \(y = k\) (Vertical shift)

Quick Check

If \(y = 3 \sin(2x)\), what is the period?

Answer: \(\frac{2\pi}{2} = \pi\)