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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![**Problem Statement: Write the Product as a Sum**
Given Expression:
\[ \cos(x) \sin(3x) \]
**Input Box:**
- The area where the solution can be entered.
**Additional Feature:**
- "Show My Work" (Optional): This section can be expanded to provide detailed steps or reasoning. It's accompanied by an information icon for further assistance.
**Submission:**
- "Submit Answer" button to enter the response.
**Explanation for Students:**
This exercise involves using trigonometric identities to transform the product of sine and cosine functions into a sum. Utilize the product-to-sum formulas in trigonometry to derive the equivalent sum expression. The relevant identity here is:
\[ \cos(A)\sin(B) = \frac{1}{2} [\sin(A + B) - \sin(A - B)] \]
Apply this identity to solve the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52bbf476-e154-4447-bb66-49220c252e1f%2Fed973f01-4370-4bed-b37d-b84c25a9a6ca%2F7h4xqeq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Write the Product as a Sum**
Given Expression:
\[ \cos(x) \sin(3x) \]
**Input Box:**
- The area where the solution can be entered.
**Additional Feature:**
- "Show My Work" (Optional): This section can be expanded to provide detailed steps or reasoning. It's accompanied by an information icon for further assistance.
**Submission:**
- "Submit Answer" button to enter the response.
**Explanation for Students:**
This exercise involves using trigonometric identities to transform the product of sine and cosine functions into a sum. Utilize the product-to-sum formulas in trigonometry to derive the equivalent sum expression. The relevant identity here is:
\[ \cos(A)\sin(B) = \frac{1}{2} [\sin(A + B) - \sin(A - B)] \]
Apply this identity to solve the problem.
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