question 8 of 10 for the function y = -2 + 5 sin(π/12(x - 2)), what is the minimum value? answer here submit
question 8 of 10 for the function y = -2 + 5 sin(π/12(x - 2)), what is the minimum value? answer here submit
Answer
Answer:
-7
Explanation:
Step1: Recall sine - function range
The range of the sine function $y = \sin(u)$ is $[- 1,1]$, i.e., $-1\leqslant\sin\left(\frac{\pi}{12}(x - 2)\right)\leqslant1$.
Step2: Find the minimum of the given function
We have $y=-2 + 5\sin\left(\frac{\pi}{12}(x - 2)\right)$. To find the minimum value of $y$, we consider the minimum value of $\sin\left(\frac{\pi}{12}(x - 2)\right)$. When $\sin\left(\frac{\pi}{12}(x - 2)\right)=-1$, we substitute this value into the function: $y=-2+5\times(-1)=-2 - 5=-7$.