Find an equation for the sine graph, f(x): fx 3 2 -360° -180° 180° 360° -1 -2 -3 -4 Write your answer in the form f(x) = A sin (Bx + C) + D, where A, B, C, and D are real numbers. f(x) %3D sin
Find an equation for the sine graph, f(x): fx 3 2 -360° -180° 180° 360° -1 -2 -3 -4 Write your answer in the form f(x) = A sin (Bx + C) + D, where A, B, C, and D are real numbers. f(x) %3D sin
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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Refer to the picture below.
![**Find an Equation for the Sine Graph, f(x):**
The goal is to determine the equation of the sine function shown in the graph. The equation should be in the form of:
\[ f(x) = A \sin(Bx + C) + D \]
where \(A\), \(B\), \(C\), and \(D\) are real numbers.
**Graph Description:**
- The graph is plotted on a Cartesian plane with \(x\)-axis ranging from \(-360^\circ\) to \(360^\circ\) and \(y\)-axis ranging from \(-4\) to \(4\).
- The graph of the sine function is drawn in purple and exhibits one full cycle between \(-360^\circ\) and \(360^\circ\).
- The wave intersects the \(y\)-axis at \(y = 0\) and has its maximum at \(y = 2\) and minimum at \(y = -2\).
- The sine wave starts from \(y = 0\) at \(x = -360^\circ\), reaches the minimum at \(x = -180^\circ\), returns to \(y = 0\) at \(x = 0\), reaches the maximum at \(x = 180^\circ\), and again returns to \(y = 0\) at \(x = 360^\circ\).
**Instructions:**
Write the equation of the sine function in the box provided below the graph. The answer should follow the specified format.
\[ f(x) = \]
Use the provided buttons to insert sine function elements such as \(\sin\), parentheses, and the degree symbol.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40d81c3d-217c-474a-b6c2-74f4c4a8c8c0%2F82562c54-3b5a-49f9-8dfd-6ef633f43d11%2Fc6caun_processed.png&w=3840&q=75)
Transcribed Image Text:**Find an Equation for the Sine Graph, f(x):**
The goal is to determine the equation of the sine function shown in the graph. The equation should be in the form of:
\[ f(x) = A \sin(Bx + C) + D \]
where \(A\), \(B\), \(C\), and \(D\) are real numbers.
**Graph Description:**
- The graph is plotted on a Cartesian plane with \(x\)-axis ranging from \(-360^\circ\) to \(360^\circ\) and \(y\)-axis ranging from \(-4\) to \(4\).
- The graph of the sine function is drawn in purple and exhibits one full cycle between \(-360^\circ\) and \(360^\circ\).
- The wave intersects the \(y\)-axis at \(y = 0\) and has its maximum at \(y = 2\) and minimum at \(y = -2\).
- The sine wave starts from \(y = 0\) at \(x = -360^\circ\), reaches the minimum at \(x = -180^\circ\), returns to \(y = 0\) at \(x = 0\), reaches the maximum at \(x = 180^\circ\), and again returns to \(y = 0\) at \(x = 360^\circ\).
**Instructions:**
Write the equation of the sine function in the box provided below the graph. The answer should follow the specified format.
\[ f(x) = \]
Use the provided buttons to insert sine function elements such as \(\sin\), parentheses, and the degree symbol.
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