Sinusoidal Function Transformations

In 3.5 we measured sinusoids — amplitude, midline, period, and frequency — and saw how $a$ and $d$ in $y = a \sin \theta + d$ control the height of a wave. But every function in 3.5 still had period $2\pi$. Real periodic data almost never cycles every $2\pi$ units: the pedal from 3.1 takes 1.2 seconds per turn. This note adds the constant that controls the period and then puts all the pieces together to write equations. Sliding a graph left or right — the last transformation — is the topic of 3.6B.