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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See attached. I need help rewriting the left side and verifying the identity. Thank you.
![### Verifying Trigonometric Identities
#### Problem Statement:
Verify the identity \(7 \sin{ (12t)} = 28 \sin{ 3t} \cos^3{ 3t} - 28 \sin^3{ 3t} \cos{ 3t} \).
---
#### Question:
Which type of identities will be the most useful for changing the argument of the function on the left side by a factor of \(\frac{1}{2}\)? Select all that apply.
- A. Quotient identities
- B. **Double-angle formulas** ✓
- C. Even-odd identities
- D. Pythagorean identities
---
#### Solution:
Rewrite the left side using one of the appropriate formulas once.
\[ 7 \sin{(12t)} = \]
---
This problem involves verifying a trigonometric identity by potentially using double-angle formulas to facilitate the transformation of arguments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3988bcd1-9898-42cb-8768-27ebf2c36c6f%2F9f6ecb44-14bb-4c8a-ab3c-6c68a2628f53%2Fe0o1z9q_processed.png&w=3840&q=75)
Transcribed Image Text:### Verifying Trigonometric Identities
#### Problem Statement:
Verify the identity \(7 \sin{ (12t)} = 28 \sin{ 3t} \cos^3{ 3t} - 28 \sin^3{ 3t} \cos{ 3t} \).
---
#### Question:
Which type of identities will be the most useful for changing the argument of the function on the left side by a factor of \(\frac{1}{2}\)? Select all that apply.
- A. Quotient identities
- B. **Double-angle formulas** ✓
- C. Even-odd identities
- D. Pythagorean identities
---
#### Solution:
Rewrite the left side using one of the appropriate formulas once.
\[ 7 \sin{(12t)} = \]
---
This problem involves verifying a trigonometric identity by potentially using double-angle formulas to facilitate the transformation of arguments.
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