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Graph each function using radians. 4) y = 4cos 0 6) y = 2cos Т Л Ө 2 2л Зл 2л 2 Зл 4 5л Зл 2 5 бл 5) y = sin 40 л л 4 2 Зл 4 л 5л 3л 4 2 4 7л 2л

Graph each function using radians. 4) y = 4cos 0 6) y = 2cos Т Л Ө 2 2л Зл 2л 2 Зл 4 5л Зл 2 5 бл 5) y = sin 40 л л 4 2 Зл 4 л 5л 3л 4 2 4 7л 2л

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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**Graph each function using radians:** **4) \( y = 4 \cos \theta \)** The graph is plotted on a standard Cartesian coordinate plane. The x-axis is labeled in increments of \(\frac{\pi}{2}\), ranging from \(-3\pi\) to \(3\pi\). The y-axis ranges from -5 to 5. This graph represents a cosine function with an amplitude of 4, which will have peaks at y = 4 and troughs at y = -4. **5) \( y = \sin 4\theta \)** This graph is also plotted on a Cartesian plane. The x-axis is labeled in increments of \(\frac{\pi}{4}\), with a range from \(-2\pi\) to \(2\pi\). The y-axis ranges from -6 to 6. The function has a period that is shorter than the standard sine function due to the coefficient of 4 in the argument, causing it to oscillate more rapidly. **6) \( y = 2 \cos \frac{\theta}{2} \)** This graph uses a similar grid. The x-axis is labeled in increments of \(\pi\) from \(-6\pi\) to \(6\pi\). The y-axis ranges from -3 to 3. This is a cosine function with a reduced frequency, resulting in a periodic wave that stretches further along the x-axis than the standard cosine function, due to the division by 2 in the argument. The amplitude is 2, creating peaks at y = 2 and troughs at y = -2.
Transcribed Image Text:**Graph each function using radians:** **4) \( y = 4 \cos \theta \)** The graph is plotted on a standard Cartesian coordinate plane. The x-axis is labeled in increments of \(\frac{\pi}{2}\), ranging from \(-3\pi\) to \(3\pi\). The y-axis ranges from -5 to 5. This graph represents a cosine function with an amplitude of 4, which will have peaks at y = 4 and troughs at y = -4. **5) \( y = \sin 4\theta \)** This graph is also plotted on a Cartesian plane. The x-axis is labeled in increments of \(\frac{\pi}{4}\), with a range from \(-2\pi\) to \(2\pi\). The y-axis ranges from -6 to 6. The function has a period that is shorter than the standard sine function due to the coefficient of 4 in the argument, causing it to oscillate more rapidly. **6) \( y = 2 \cos \frac{\theta}{2} \)** This graph uses a similar grid. The x-axis is labeled in increments of \(\pi\) from \(-6\pi\) to \(6\pi\). The y-axis ranges from -3 to 3. This is a cosine function with a reduced frequency, resulting in a periodic wave that stretches further along the x-axis than the standard cosine function, due to the division by 2 in the argument. The amplitude is 2, creating peaks at y = 2 and troughs at y = -2.
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