Answered: Determine the amplitude, midline,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.5: Trigonometric Graphs

Problem 25E

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Question

Determine the amplitude, midline, period, and an equation involving the sine function for the graph shown below.

Expert Solution

Step 1: Given information and basic information

Given information:

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Aim:

Basic information:

The amplitude (A) is defined as the height from the center line to the peak ( or trough ).
The midline (D) is defined as the horizontal axis that is used as the reference line about the graph of a periodic function oscillates.
The period (T) is defined as the length from one peak to the next peak of the periodic function.

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The graph for the sinusoidal function is described below with amplitude , midline and period.

$\begin{array}{rcl} y & = & A \sin (B (x - C)) + D, w h e r e (1) \\ A & = & A m p l i t u d e = (\frac{(y_{m a x} - y_{m i n})}{2}) (2) \\ B & = & \frac{2 π}{T}, w h e r e T = P e r i o d (3) \\ C & = & h o r i z o n t a l s h i f t \\ D & = & m i d l i n e = (\frac{(y_{m a x} + y_{m i n})}{2}) (4) \end{array} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -$

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