## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$y=2 \ \sin (2x+4)$
The general form for the sinusoidal function can be expressed as: $y=A\sin{(\omega x-\phi)}+B ..(1)$ where $A$ is the amplitude and $B$ represents the vertical shift. The $\omega$ can be found from the period by the formula: $\omega=\dfrac{2\pi}{T}$ and the phase shift is $\dfrac{\phi}{\omega}$. This means that $\phi=\omega \times \ Phase \ Shift$ We have: $A=2$, $B=0$, $\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{ \pi}=2$ $\phi=(2)(-2)=-4$ Therefore, our sinusoidal function (1) becomes: $y=2 \ \sin (2x+4)$