question determine the minimum and maximum value of the following trigonometric function. f(x)=-5cos(1/3x)-5…

Answer:

Minimum: -10, Maximum: 0

Explanation:

Step1: Recall cosine range

The range of $\cos(t)$ is $[- 1,1]$, here $t=\frac{1}{3}x$.

Step2: Analyze the function with coefficient

For $y = - 5\cos(\frac{1}{3}x)-5$, when $\cos(\frac{1}{3}x)=1$, we have $y=-5\times1 - 5=-10$ (minimum).

Step3: Analyze the function for maximum

When $\cos(\frac{1}{3}x)=-1$, we have $y=-5\times(-1)-5 = 0$ (maximum).