Question

graph $g(t) = 4sin(3t) + 2$.
use 3.14 for $pi$.
use the sine tool to graph the function. the first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Explanation:

Step1: Identify midline

The midline of \(g(t) = A\sin(Bt) + C\) is \(y = C\). Here, \(C = 2\), so midline is \(y=2\). At \(t=0\), \(g(0)=4\sin(0)+2=2\), so first point is (0,2).

Step2: Find closest max/min

The period is \(T=\frac{2\pi}{B}=\frac{2\times3.14}{3}\approx2.093\). The first maximum occurs at \(Bt=\frac{\pi}{2}\), so \(t=\frac{\pi}{2B}=\frac{3.14}{2\times3}\approx0.523\). At this \(t\), \(g(t)=4\times1 + 2=6\), so second point is (0.523,6).

Answer:

First point: (0, 2); Second point: (0.523, 6)