Look at the picture. Please show the steps. The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.The graph is a sinusoidal wave, likely representing a cosine or sine function. It oscillates vertically between -6 and 6 on the y-axis. The period of the wave can be determined from its x-intercepts, which occur at $ x = \frac{\pi}{20} $, $ x = \frac{3\pi}{20} $, $ x = \frac{7\pi}{20} $, and $ x = \frac{9\pi}{20} $.There is an x-axis symmetry, indicating that it might be a cosine wave, given the peaks and troughs align with key x-coordinates.**Equation:**A general form for the equation is $ y = a \cos(b(x - c)) + d $, where:- $ a $ adjusts the amplitude- $ b $ adjusts the period- $ c $ shifts the graph horizontally- $ d $ shifts the graph verticallyAnalyze the graph to determine specific values for these parameters based on the given x-values for peaks, troughs, and intercepts.

Answered: The following graph shows at least one…

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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Look at the picture. Please show the steps.

The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

The graph is a sinusoidal wave, likely representing a cosine or sine function. It oscillates vertically between -6 and 6 on the y-axis. The period of the wave can be determined from its x-intercepts, which occur at $ x = \frac{\pi}{20} $, $ x = \frac{3\pi}{20} $, $ x = \frac{7\pi}{20} $, and $ x = \frac{9\pi}{20} $.

There is an x-axis symmetry, indicating that it might be a cosine wave, given the peaks and troughs align with key x-coordinates.

**Equation:**
A general form for the equation is $ y = a \cos(b(x - c)) + d $, where:
- $ a $ adjusts the amplitude
- $ b $ adjusts the period
- $ c $ shifts the graph horizontally
- $ d $ shifts the graph vertically

Analyze the graph to determine specific values for these parameters based on the given x-values for peaks, troughs, and intercepts.

Expert Solution

Step 1

Consider the given graph.

The given graph is similar to graph of sine function.

Hence, the equation of the given graph can be represented by the equation of a sine function of the form $y = A \sin (B (x - C)) + D$ where A is the amplitude, B is given by $\frac{2 π}{p e r i o d}$ , C is the phase shift and D is the vertical shift.

The amplitude of a sinusoidal function is given by the vertical distance from the sinusoidal axis and the highest point on the graph.

Consider the following figure.

The sinusoidal axis is the x-axis given by $y = 0$ .

The highest point has y value 6.

Hence, the vertical distance between the sinusoidal axis and 6 is 6.

Thus, the amplitude A = 6.

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