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2) Graph the function: y = 3 sin 20

2) Graph the function: y = 3 sin 20

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:** --- **Exercise 2:** Graph the function: \( y = 3 \sin 2\theta \) **Graph Description:** The graph provided is a blank grid that can be used to plot trigonometric functions like \( y = 3 \sin 2\theta \). ### Steps for Graphing: 1. **Identify the Function Components:** - Amplitude: 3 (This is the coefficient of the sine function, indicating the peak vertical distance from the midline.) - Frequency: 2 (This number inside the sine function determines how many cycles the sine wave completes in a specific interval.) - Period: \( \frac{2\pi}{2} = \pi \) (The period is calculated by dividing \( 2\pi \) by the frequency, showing one complete cycle of the wave.) 2. **Plot the Key Points:** - Start at \((0, 0)\). - The next key points up to one period \((\pi)\) could include: - Maximum at \((\frac{\pi}{4}, 3)\) - Crossing zero at \((\frac{\pi}{2}, 0)\) - Minimum at \((\frac{3\pi}{4}, -3)\) - Back to zero at \((\pi, 0)\) 3. **Continue the Pattern:** - Repeat every \(\pi\) radians to extend the graph across the grid. ### Visualization Tips: - Make sure to label the x-axis in terms of \(\theta\) and y-axis appropriately. - Note that the graph should have a repeating wave pattern due to the sine function, with alternating cycles above and below the axis at intervals defined by the period. By following these steps, the graph will accurately represent the function \( y = 3 \sin 2\theta \).
Transcribed Image Text:**Transcription for Educational Website:** --- **Exercise 2:** Graph the function: \( y = 3 \sin 2\theta \) **Graph Description:** The graph provided is a blank grid that can be used to plot trigonometric functions like \( y = 3 \sin 2\theta \). ### Steps for Graphing: 1. **Identify the Function Components:** - Amplitude: 3 (This is the coefficient of the sine function, indicating the peak vertical distance from the midline.) - Frequency: 2 (This number inside the sine function determines how many cycles the sine wave completes in a specific interval.) - Period: \( \frac{2\pi}{2} = \pi \) (The period is calculated by dividing \( 2\pi \) by the frequency, showing one complete cycle of the wave.) 2. **Plot the Key Points:** - Start at \((0, 0)\). - The next key points up to one period \((\pi)\) could include: - Maximum at \((\frac{\pi}{4}, 3)\) - Crossing zero at \((\frac{\pi}{2}, 0)\) - Minimum at \((\frac{3\pi}{4}, -3)\) - Back to zero at \((\pi, 0)\) 3. **Continue the Pattern:** - Repeat every \(\pi\) radians to extend the graph across the grid. ### Visualization Tips: - Make sure to label the x-axis in terms of \(\theta\) and y-axis appropriately. - Note that the graph should have a repeating wave pattern due to the sine function, with alternating cycles above and below the axis at intervals defined by the period. By following these steps, the graph will accurately represent the function \( y = 3 \sin 2\theta \).
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