Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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### Geometric Transformation Identification Determine what geometric transformation is needed to obtain the graph of the second function from the graph of the first one. #### Transformations: **a)** For \( y = \sin(x) \) to \( y = \sin(0.3x) \) **b)** For \( y = \cos(5x) \) to \( y = \cos(5x-\pi) \) **c)** For \( y = \tan(3x) \) to \( y = \tan(-3x) \) **d)** For \( y = -\cot(x/2) \) to \( y = \cot(x/2) \) **e)** For \( y = 3\sin(x) \) to \( y = 6\sin(x) \) **f)** For \( y = \cos(3x) \) to \( y = \cos(4x) \) Each option presents a pair of trigonometric functions, and your task is to identify the type of geometric transformation applied, such as translation, reflection, stretching, or compression, to obtain the second function from the first.
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Transcribed Image Text:### Geometric Transformation Identification Determine what geometric transformation is needed to obtain the graph of the second function from the graph of the first one. #### Transformations: **a)** For \( y = \sin(x) \) to \( y = \sin(0.3x) \) **b)** For \( y = \cos(5x) \) to \( y = \cos(5x-\pi) \) **c)** For \( y = \tan(3x) \) to \( y = \tan(-3x) \) **d)** For \( y = -\cot(x/2) \) to \( y = \cot(x/2) \) **e)** For \( y = 3\sin(x) \) to \( y = 6\sin(x) \) **f)** For \( y = \cos(3x) \) to \( y = \cos(4x) \) Each option presents a pair of trigonometric functions, and your task is to identify the type of geometric transformation applied, such as translation, reflection, stretching, or compression, to obtain the second function from the first.
The image shows a multiple-choice question related to transformations of trigonometric functions. Here's the transcription: --- "Given the function from the graph of the first: (a) \( y = \sin(x) \), \( y = \sin(0.3x) \)" Below is a selection list with the following transformation options: - reflection about the x-axis - reflection about the y-axis - horizontal stretch - vertical stretch - horizontal shrink - vertical shrink - horizontal translation - vertical translation Another pair of functions is presented: "(e) \( y = 3\sin(x) \), \( y = 6\sin(x) \)" --- This text appears to be part of an educational exercise focusing on how different transformations affect the graphs of sine functions.
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Transcribed Image Text:The image shows a multiple-choice question related to transformations of trigonometric functions. Here's the transcription: --- "Given the function from the graph of the first: (a) \( y = \sin(x) \), \( y = \sin(0.3x) \)" Below is a selection list with the following transformation options: - reflection about the x-axis - reflection about the y-axis - horizontal stretch - vertical stretch - horizontal shrink - vertical shrink - horizontal translation - vertical translation Another pair of functions is presented: "(e) \( y = 3\sin(x) \), \( y = 6\sin(x) \)" --- This text appears to be part of an educational exercise focusing on how different transformations affect the graphs of sine functions.
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