question 3 of 10 for the function y = -2 + 5 sin (π/12(x - 2)), what is the minimum value? answer here
question 3 of 10 for the function y = -2 + 5 sin (π/12(x - 2)), what is the minimum value? answer here
Answer
Explanation:
Step1: Recall sine - function range
The range of the sine function $y = \sin(u)$ is $[- 1,1]$. Here $u=\frac{\pi}{12}(x - 2)$.
Step2: Find the minimum of the given function
We have $y=-2 + 5\sin(\frac{\pi}{12}(x - 2))$. To find the minimum value of $y$, we consider the minimum value of $\sin(\frac{\pi}{12}(x - 2))$. The minimum value of $\sin(\frac{\pi}{12}(x - 2))=-1$. Substitute $\sin(\frac{\pi}{12}(x - 2))=-1$ into the function $y=-2 + 5\sin(\frac{\pi}{12}(x - 2))$: $y=-2+5\times(-1)$. $y=-2 - 5=-7$.
Answer:
$-7$