Graphs of trig functions

A sinusoidal function has the form \(f(x)=a\sin(b(x-h))+k\) or \(f(x)=a\cos(b(x-h))+k\). The amplitude is \(|a|\), the vertical distance from the midline to a peak. The midline is the horizontal line \(y=k\). The period is \(\frac{2\pi}{|b|}\), the horizontal length of one full cycle. The phase shift is \(h\): positive shifts right, negative shifts left. Vertical stretch occurs when \(|a|>1\); vertical compression occurs when \(0<|a|<1\).