for the function y = -2 + 5 sin(π/12(x - 2)), what is the maximum value? answer here

Answer:

3

Explanation:

Step1: Recall sine - function range

The range of $\sin t$ is $[- 1,1]$. Here $t=\frac{\pi}{12}(x - 2)$.

Step2: Find maximum of $5\sin t$

When $\sin t = 1$, the value of $5\sin t$ is maximized. So, $5\sin t_{max}=5\times1 = 5$.

Step3: Calculate maximum of $y$

We have $y=-2 + 5\sin t$. Substituting the maximum value of $5\sin t$ into the function, we get $y_{max}=-2 + 5=3$.