In the standard $(x,y)$ coordinate plane, the graph of the equation $y=3\sin{(2x+0.5\pi)}$ has what amplitude and period?

$$\begin{array}{l c c} & \underline{\text{amplitude}} & \underline{\text{period}} \\ \text{A.} & 3 & \pi \\ \text{B.} & 3 & 2\pi \\ \text{C.} & 3 & 4\pi \\ \text{D.} & 6 & \pi \\ \text{E.} & 6 & 2\pi \\ \end{array}$$

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The standard equation for a trigonometric function is:

$$y=A\sin{B(x-C)}+D$$

The amplitude is $A$ and the period is related to $B$ by:

$$\text{Period} = \frac{2\pi}{B}$$

Rewriting the given equation:

$$y=3\sin{(2x+0.5\pi)}$$ $$y = 3\sin{2(x+0.25\pi)}$$

In this form we can see that the amplitude is 3 and the period is:

$$\text{Period} = \frac{2\pi}{B}$$ $$\text{Period} = \frac{2\pi}{2}$$ $$\text{Period} =\pi$$