question 2 (1 point)\nwhat are the maximum and minimum values of the fuction y = - 2 sin(x - 30°)\nmaximum…

question 2 (1 point)\nwhat are the maximum and minimum values of the fuction y = - 2 sin(x - 30°)\nmaximum 0, minimum -4\nmaximum 2, minimum -2\nmaximum 4, minimum 0\nmaximum 4, minimum 2

question 2 (1 point)\nwhat are the maximum and minimum values of the fuction y = - 2 sin(x - 30°)\nmaximum 0, minimum -4\nmaximum 2, minimum -2\nmaximum 4, minimum 0\nmaximum 4, minimum 2

Answer

Explanation:

Step1: Recall sine - function range

The range of the sine function $y = \sin(u)$ is $- 1\leqslant\sin(u)\leqslant1$. Here $u=x - 30^{\circ}$, so $-1\leqslant\sin(x - 30^{\circ})\leqslant1$.

Step2: Multiply by - 2

When we multiply the inequality $-1\leqslant\sin(x - 30^{\circ})\leqslant1$ by $-2$, we need to reverse the inequality signs. We get $(-2)\times(-1)\geqslant-2\sin(x - 30^{\circ})\geqslant(-2)\times1$.

Step3: Simplify the inequality

$2\geqslant-2\sin(x - 30^{\circ})\geqslant - 2$.

Answer:

B. maximum 2, minimum - 2