The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph.Hint: Think about the general form of the trig function and find the constants A: amplitude, B: period, C: phase(Horizontal) shift, D: Vertical Shift from the graph.You can check your final answer by plotting the function that you build and comparing it with your given function. Provide as many details as possible. The image displays a graph of a trigonometric function, specifically a sine wave. The axes are labeled $x$ and $y$.### Graph Details:- **XAxis (Horizontal)**: - The x-axis is marked with increments of $\frac{\pi}{4}$ up to $\pi$. - Key points are labeled as $\frac{\pi}{4}$, $\frac{\pi}{2}$, $\frac{3\pi}{4}$, and $\pi$.- **YAxis (Vertical)**: - The y-axis ranges from -10 to 10, with marks at every 2 units.### Sine Wave Description:- The sine wave starts at the origin (0,0).- It reaches a maximum value slightly below $\frac{\pi}{4}$.- It crosses the x-axis at $\frac{\pi}{2}$.- It reaches a minimum value slightly below $\frac{3\pi}{4}$.- The wave again crosses the x-axis at $\pi$.This graph illustrates the periodic nature of sine functions, showing one complete cycle from 0 to $\pi$.

Make the following observation: The graph is sinusoidal with maximum value as 2 and minimum value as…

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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 graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph.

Hint: Think about the general form of the trig function and find the constants A: amplitude, B: period, C: phase(Horizontal) shift, D: Vertical Shift from the graph.

You can check your final answer by plotting the function that you build and comparing it with your given function. Provide as many details as possible.

The image displays a graph of a trigonometric function, specifically a sine wave. The axes are labeled $x$ and $y$.

### Graph Details:
- **XAxis (Horizontal)**:
- The x-axis is marked with increments of $\frac{\pi}{4}$ up to $\pi$.
- Key points are labeled as $\frac{\pi}{4}$, $\frac{\pi}{2}$, $\frac{3\pi}{4}$, and $\pi$.

- **YAxis (Vertical)**:
- The y-axis ranges from -10 to 10, with marks at every 2 units.

### Sine Wave Description:
- The sine wave starts at the origin (0,0).
- It reaches a maximum value slightly below $\frac{\pi}{4}$.
- It crosses the x-axis at $\frac{\pi}{2}$.
- It reaches a minimum value slightly below $\frac{3\pi}{4}$.
- The wave again crosses the x-axis at $\pi$.

This graph illustrates the periodic nature of sine functions, showing one complete cycle from 0 to $\pi$.

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