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The graph below includes 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. y =

The graph below includes 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. y =

Advanced Engineering Mathematics
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 includes 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.
y = 

 
 
The image displays a graph of a trigonometric function, likely related to a cosine or a related function, within the Cartesian coordinate system. ### Components of the Graph: 1. **Axes:** - The horizontal axis is labeled as the \(x\)-axis. - The vertical axis is labeled as the \(y\)-axis. 2. **Plot Details:** - The graph features a red curve, which is a downward-opening parabola. - This curve is symmetric about the \(y\)-axis, touching the \(x\)-axis at two points: \(x = -\pi/3\) and \(x = \pi/3\). - The vertex of the parabola is located at \((0, -20)\). 3. **Scale and Labels:** - The \(x\)-axis is marked with values including \(-\pi/3\) and \(\pi/3\). - The \(y\)-axis includes a range of values, marked from \(-20\) upwards to \(5\). ### Interpretation: The graph suggests a quadratic relationship, likely showing the shape of a standard or a trigonometric quadratic function, possibly related to a negative cosine function that has been scaled and shifted downwards. The domain is between \(-\pi/3\) and \(\pi/3\), and the range extends from \(y = -20\) up to the \(x\)-axis.
Transcribed Image Text:The image displays a graph of a trigonometric function, likely related to a cosine or a related function, within the Cartesian coordinate system. ### Components of the Graph: 1. **Axes:** - The horizontal axis is labeled as the \(x\)-axis. - The vertical axis is labeled as the \(y\)-axis. 2. **Plot Details:** - The graph features a red curve, which is a downward-opening parabola. - This curve is symmetric about the \(y\)-axis, touching the \(x\)-axis at two points: \(x = -\pi/3\) and \(x = \pi/3\). - The vertex of the parabola is located at \((0, -20)\). 3. **Scale and Labels:** - The \(x\)-axis is marked with values including \(-\pi/3\) and \(\pi/3\). - The \(y\)-axis includes a range of values, marked from \(-20\) upwards to \(5\). ### Interpretation: The graph suggests a quadratic relationship, likely showing the shape of a standard or a trigonometric quadratic function, possibly related to a negative cosine function that has been scaled and shifted downwards. The domain is between \(-\pi/3\) and \(\pi/3\), and the range extends from \(y = -20\) up to the \(x\)-axis.
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