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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![**Write the sum as a product:**
\[
\cos(20.4w) - \cos(9.4w) =
\]
In this exercise, you are asked to express the difference of cosines, \(\cos(20.4w) - \cos(9.4w)\), as a product using trigonometric identities. The difference of cosines can be represented as a product using the appropriate trigonometric identity:
\[
\cos A - \cos B = -2 \sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)
\]
Applying this identity to the given expression:
- Let \(A = 20.4w\) and \(B = 9.4w\).
Thus, the difference can be rewritten as:
\[
-2 \sin \left( \frac{20.4w + 9.4w}{2} \right) \sin \left( \frac{20.4w - 9.4w}{2} \right)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F987fdeb2-ff61-48e7-b9d1-28b1acd386ad%2F94853460-9cca-43eb-ac1c-dc96d4960bc3%2Flge2dw_processed.png&w=3840&q=75)
Transcribed Image Text:**Write the sum as a product:**
\[
\cos(20.4w) - \cos(9.4w) =
\]
In this exercise, you are asked to express the difference of cosines, \(\cos(20.4w) - \cos(9.4w)\), as a product using trigonometric identities. The difference of cosines can be represented as a product using the appropriate trigonometric identity:
\[
\cos A - \cos B = -2 \sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)
\]
Applying this identity to the given expression:
- Let \(A = 20.4w\) and \(B = 9.4w\).
Thus, the difference can be rewritten as:
\[
-2 \sin \left( \frac{20.4w + 9.4w}{2} \right) \sin \left( \frac{20.4w - 9.4w}{2} \right)
\]
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