what is the range of y = -5sin(x)?\no all real numbers -5≤y≤5\no all real numbers -\\frac{5}{2}≤y≤\\frac{5}{2…

Explanation:

Step1: Recall range of basic sine function

The range of $y = \sin(x)$ is $- 1\leqslant\sin(x)\leqslant1$.

Step2: Consider the transformation

We have $y=-5\sin(x)$. Multiply each part of the inequality $-1\leqslant\sin(x)\leqslant1$ by $- 5$. When we multiply an inequality by a negative number, the direction of the inequality signs changes. So $(-5)\times1\leqslant - 5\sin(x)\leqslant(-5)\times(-1)$.

Step3: Simplify the inequality

We get $-5\leqslant y\leqslant5$.

Answer:

all real numbers $-5\leqslant y\leqslant5$