The function shown in the graph can be written as y = a sin (b (x - h)) + k, where a is positive. The graph shows values between -2mand 2 T.AY-6-54-32141 23456a. What is the amplitude?b. What is the period.?c. What is the horizontal shift?d. What is the centerline (the vertical shift)?e. Write the function represented.

Answered: The function shown in the graph can be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The function shown in the graph can be written as y = a sin (b (x - h)) + k, where a is positive. The graph shows values between -2m
and 2 T.
AY
-6-54-32141 23456
a. What is the amplitude?
b. What is the period.?
c. What is the horizontal shift?
d. What is the centerline (the vertical shift)?
e. Write the function represented.

Expert Solution

Step 1

To find the amplitude, measure the distance between the upper and lower peak of the curve and then divide by 2.

$\begin{array}{rcl} A m p l i t u d e & = & \frac{5 - 1}{2} \\ a & = & \frac{4}{2} \\ = & 2 \end{array}$

Therefore, the amplitude is $a = 2$ .

Step 2

To obtain the period, find the length of one complete cycle. Also find b from the period, $P = \frac{2 π}{b}$ .

$\begin{array}{rcl} P e r i o d & = & 2 π - (- 2 π) \\ P & = & 2 π + 2 π \\ = & 4 π \\ \frac{2 π}{b} & = & 4 π \\ \frac{2 π}{4 π} & = & b \\ \frac{1}{2} & = & b \end{array}$

Hence, the period is $P = 4 π$ and $b = \frac{1}{2}$ .

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