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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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 =
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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