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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Question
![**Problem Statement:**
Write the sum as a product:
\[
\sin(5.2r) - \sin(3.6r) = \, \text{[Answer Box]}
\]
**Explanation:**
This problem involves using a trigonometric identity to convert a difference of sines into a product. The identity applied here is:
\[
\sin A - \sin B = 2 \cos\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)
\]
**Solution Steps:**
1. Identify \( A = 5.2r \) and \( B = 3.6r \).
2. Calculate \(\frac{A + B}{2}\) and \(\frac{A - B}{2}\):
- \(\frac{5.2r + 3.6r}{2} = \frac{8.8r}{2} = 4.4r\)
- \(\frac{5.2r - 3.6r}{2} = \frac{1.6r}{2} = 0.8r\)
3. Substitute into the identity:
- \(2 \cos(4.4r) \sin(0.8r)\)
Thus, the expression \(\sin(5.2r) - \sin(3.6r)\) can be rewritten as the product:
\[
2 \cos(4.4r) \sin(0.8r)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c16c5d2-e997-4e04-a749-57ee722e7387%2Fa5758f58-697a-4b11-b73a-96f00c19d2a8%2Fsxggtpi_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write the sum as a product:
\[
\sin(5.2r) - \sin(3.6r) = \, \text{[Answer Box]}
\]
**Explanation:**
This problem involves using a trigonometric identity to convert a difference of sines into a product. The identity applied here is:
\[
\sin A - \sin B = 2 \cos\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)
\]
**Solution Steps:**
1. Identify \( A = 5.2r \) and \( B = 3.6r \).
2. Calculate \(\frac{A + B}{2}\) and \(\frac{A - B}{2}\):
- \(\frac{5.2r + 3.6r}{2} = \frac{8.8r}{2} = 4.4r\)
- \(\frac{5.2r - 3.6r}{2} = \frac{1.6r}{2} = 0.8r\)
3. Substitute into the identity:
- \(2 \cos(4.4r) \sin(0.8r)\)
Thus, the expression \(\sin(5.2r) - \sin(3.6r)\) can be rewritten as the product:
\[
2 \cos(4.4r) \sin(0.8r)
\]
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