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Write an equation of the form y=a sinbx or y = a cos bx to describe the graph below. JT OsinO OcosO D=0 olo

Write an equation of the form y=a sinbx or y = a cos bx to describe the graph below. JT OsinO OcosO D=0 olo

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription for Educational Website:** --- ### Writing Trigonometric Equations **Objective:** Write an equation of the form \( y = a \sin bx \) or \( y = a \cos bx \) to describe the graph. #### Graph Analysis - **Graph Description:** - The graph is a blue sinusoidal curve. - It has a wave pattern that repeats periodically. - The x-axis is labeled with fractions of \( \pi \), specifically: \(-\pi/3\), \(\pi/6\), \(\pi/2\), \(\pi\), \(3\pi/2\), \(5\pi/3\). - **Axes Information:** - The y-axis ranges from -2 to 2. - The periodic nature suggests a sine or cosine function. **Interactive Elements:** - **Equation Input Box:** - There is a text box provided to enter the equation that describes the graph. - **Symbol Pallet:** - Includes symbols for trigonometric functions (\(\sin\), \(\cos\)), pi (\(\pi\)), and other mathematical operators. **Instructions:** 1. **Analyze the Graph** - Determine the amplitude, frequency, and phase shift. - Identify key points where the graph crosses the axes and reaches its maxima/minima. 2. **Choose the Function** - Decide whether to use a sine or cosine function based on the graph's starting position. 3. **Formulate the Equation** - Use the identified parameters to write the equation of the form \( y = a \sin bx \) or \( y = a \cos bx \). --- **Note:** This exercise helps in understanding the properties of trigonometric functions and their graphical representations.
Transcribed Image Text:**Transcription for Educational Website:** --- ### Writing Trigonometric Equations **Objective:** Write an equation of the form \( y = a \sin bx \) or \( y = a \cos bx \) to describe the graph. #### Graph Analysis - **Graph Description:** - The graph is a blue sinusoidal curve. - It has a wave pattern that repeats periodically. - The x-axis is labeled with fractions of \( \pi \), specifically: \(-\pi/3\), \(\pi/6\), \(\pi/2\), \(\pi\), \(3\pi/2\), \(5\pi/3\). - **Axes Information:** - The y-axis ranges from -2 to 2. - The periodic nature suggests a sine or cosine function. **Interactive Elements:** - **Equation Input Box:** - There is a text box provided to enter the equation that describes the graph. - **Symbol Pallet:** - Includes symbols for trigonometric functions (\(\sin\), \(\cos\)), pi (\(\pi\)), and other mathematical operators. **Instructions:** 1. **Analyze the Graph** - Determine the amplitude, frequency, and phase shift. - Identify key points where the graph crosses the axes and reaches its maxima/minima. 2. **Choose the Function** - Decide whether to use a sine or cosine function based on the graph's starting position. 3. **Formulate the Equation** - Use the identified parameters to write the equation of the form \( y = a \sin bx \) or \( y = a \cos bx \). --- **Note:** This exercise helps in understanding the properties of trigonometric functions and their graphical representations.
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