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The following graph f(0) = cose depicts how many cycles of cosine? K -2T оо O ... -1.5m 01/2 01/1/20 0¹ O -T -0.5 0.5 -0.5 10 0.5 1.5m 2n

The following graph f(0) = cose depicts how many cycles of cosine? K -2T оо O ... -1.5m 01/2 01/1/20 0¹ O -T -0.5 0.5 -0.5 10 0.5 1.5m 2n

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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**Educational Content: Understanding Cosine Graphs** ### Graph Analysis of \( f(\theta) = \cos(\theta) \) **Question:** The following graph \( f(\theta) = \cos(\theta) \) depicts how many cycles of cosine? **Graph Explanation:** The graph shown is a plot of the cosine function \( f(\theta) = \cos(\theta) \). The horizontal axis represents the angle \( \theta \) measured in radians, and the vertical axis represents the value of \( \cos(\theta) \). The graph extends from \( -2\pi \) to \( 2\pi \) on the horizontal axis and from -1 to 1 on the vertical axis. Key observations: - The graph starts at \( \theta = -2\pi \). - The graph completes one full cycle by reaching \( 0 \pi \) and continues to complete another full cycle by \( 2\pi \). In the interval \( -2\pi \) to \( 2\pi \), the graph of \( f(\theta) = \cos(\theta) \) completes exactly two cycles. **Options:** - \( \bigcirc \; 2 \) - \( \bigcirc \; \frac{1}{2} \) - \( \bigcirc \; 1\frac{1}{2} \) - \( \bigcirc \; 1 \) **Correct Answer:** The graph depicts **2** cycles of the cosine function \( f(\theta) = \cos(\theta) \). Understanding the behavior of the cosine function over different intervals helps in solving various trigonometric problems. This visualization reaffirms that the cosine function has a period of \( 2\pi \), completing one full cycle over every \( 2\pi \) interval.
Transcribed Image Text:**Educational Content: Understanding Cosine Graphs** ### Graph Analysis of \( f(\theta) = \cos(\theta) \) **Question:** The following graph \( f(\theta) = \cos(\theta) \) depicts how many cycles of cosine? **Graph Explanation:** The graph shown is a plot of the cosine function \( f(\theta) = \cos(\theta) \). The horizontal axis represents the angle \( \theta \) measured in radians, and the vertical axis represents the value of \( \cos(\theta) \). The graph extends from \( -2\pi \) to \( 2\pi \) on the horizontal axis and from -1 to 1 on the vertical axis. Key observations: - The graph starts at \( \theta = -2\pi \). - The graph completes one full cycle by reaching \( 0 \pi \) and continues to complete another full cycle by \( 2\pi \). In the interval \( -2\pi \) to \( 2\pi \), the graph of \( f(\theta) = \cos(\theta) \) completes exactly two cycles. **Options:** - \( \bigcirc \; 2 \) - \( \bigcirc \; \frac{1}{2} \) - \( \bigcirc \; 1\frac{1}{2} \) - \( \bigcirc \; 1 \) **Correct Answer:** The graph depicts **2** cycles of the cosine function \( f(\theta) = \cos(\theta) \). Understanding the behavior of the cosine function over different intervals helps in solving various trigonometric problems. This visualization reaffirms that the cosine function has a period of \( 2\pi \), completing one full cycle over every \( 2\pi \) interval.
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