Chapter 12.8, Problem 44PPS

To determine

Find the coordinate that represents a maximum for each graph.

Answer to Problem 44PPS

The coordinate for maximum value is $(\frac{\pi }{6},4)$ .

Explanation of Solution

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

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 $y=4\sin (x+\frac{\pi }{3})$ .

Since, the y − maximum is $4$ , the x coordinate there would be $\frac{\pi }{2}$ This function is moved $\frac{\pi }{3}$ to the left, so subtract that from $\frac{\pi }{2}$ .

  $\frac{\pi }{2}-\frac{\pi }{3}=\frac{3\pi -2\pi }{6}=\frac{\pi }{6}$

Since, in a normal sine function, $(\frac{\pi }{2},1)$ is a maximum. This function is moved to the left $\frac{\pi }{3}$ , and has an amplitude of $4$ .

So, the maximum value be

  $(\frac{\pi }{6},4)$ .

Conclusion:

The maximum value is $(\frac{\pi }{6},4)$ .