determine the minimum and maximum value of the following trigonometric function. f(x)=-3 cos x

Answer:

The minimum value is - 3, the maximum value is 3.

Explanation:

Step1: Recall the range of cosine function

The range of $y = \cos x$ is $[-1,1]$, i.e., $-1\leqslant\cos x\leqslant1$.

Step2: Multiply by - 3

When we multiply the inequality $-1\leqslant\cos x\leqslant1$ by - 3, we need to reverse the inequality signs. So we get $(-3)\times1\leqslant - 3\cos x\leqslant(-3)\times(-1)$.

Step3: Simplify the inequality

We have $-3\leqslant - 3\cos x\leqslant3$. So the minimum value of $f(x)=-3\cos x$ is - 3 and the maximum value is 3.