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:**
1) Find all real solutions to the equation below. Hint: use the double angle formula.
\[\sin(2\theta) = \cos(\theta)\]
**Explanation:**
To solve this equation, we can use the double angle identity for sine, which states:
\[\sin(2\theta) = 2\sin(\theta)\cos(\theta)\]
Substituting this identity into the original equation gives:
\[2\sin(\theta)\cos(\theta) = \cos(\theta)\]
This equation can be solved by factoring or using trigonometric identities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3f56dff-0b60-49cc-8c03-28401888e8a6%2F7b0e1c5f-91a3-4ce2-8af1-96f9a06133c2%2F24notig_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1) Find all real solutions to the equation below. Hint: use the double angle formula.
\[\sin(2\theta) = \cos(\theta)\]
**Explanation:**
To solve this equation, we can use the double angle identity for sine, which states:
\[\sin(2\theta) = 2\sin(\theta)\cos(\theta)\]
Substituting this identity into the original equation gives:
\[2\sin(\theta)\cos(\theta) = \cos(\theta)\]
This equation can be solved by factoring or using trigonometric identities.
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