Chapter 13.8, Problem 46PPS

To determine

Find the coordinate that represents a maximum for each graph.

Answer to Problem 46PPS

The coordinate for maximum value is $(-\frac{\pi }{4},-1)$ .

Explanation of Solution

Given: It is given in the question that the equation is $y=-3\sin (x-\frac{\pi }{4})-4$ .

Concept Used:

In this, use the concept of understanding the equation and find out the maximum and minimum by observing the equation.

Calculation: Here, the given equation is $y=-3\sin (x-\frac{\pi }{4})-4$ .It is a sine function.

Since, the maximum y occurs when the graph is at the value of the amplitude, plus the value of the midline that gives $-1$ .

The value of the x at the maximum could ordinarily be $\frac{\pi }{4}$ , if sine were at the origin and not negative because sine is negative the maximum closet to the origin is usually the minimum when the graph is positive.

The maximum will occur $\frac{1}{4}$ of a period to the left of the center. In this case, center is $\frac{\pi }{4}$ , so the maximum is $\frac{\pi }{4}-\frac{\pi }{2}=\frac{\pi -2\pi }{4}=-\frac{\pi }{4}$

So, the maximum value is $(-\frac{\pi }{4},-1)$ .

Conclusion:

The maximum value is $(-\frac{\pi }{4},-1)$ .