Using the sum and difference of cosines formula, find the exact value of cos (5). Enclose numerators and denominators in parentheses For example (a. b)/ (14 n)
Using the sum and difference of cosines formula, find the exact value of cos (5). Enclose numerators and denominators in parentheses For example (a. b)/ (14 n)
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:**
Using the sum and difference of cosines formula, find the exact value of \( \cos \left( \frac{\pi}{12} \right) \).
**Instructions:**
Enclose numerators and denominators in parentheses. For example, express as \((a - b)/(1 + n)\).
**Interactive Input Box:**
- The box provided allows for input of mathematical expressions using buttons for various functions such as exponentiation \( a^b \), sine function \( \sin(a) \), and alpha notation \( \alpha \).
**Task:**
\[ \cos \left( \frac{\pi}{12} \right) = \]
**Note:**
Show your work and explain, in your own words, how you arrived at your answer.
---
**Hints for Solving:**
You can use the identity for the cosine of a sum or difference:
\[
\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b
\]
Consider breaking down \( \frac{\pi}{12} \) using known angles like \( \frac{\pi}{6} \), \( \frac{\pi}{4} \), \( \frac{\pi}{3} \), etc.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fb6fbe8-c93b-4e2e-8100-eedf21471e21%2Fa660a40e-673f-4126-bf78-85babf669991%2F8az9t7_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Using the sum and difference of cosines formula, find the exact value of \( \cos \left( \frac{\pi}{12} \right) \).
**Instructions:**
Enclose numerators and denominators in parentheses. For example, express as \((a - b)/(1 + n)\).
**Interactive Input Box:**
- The box provided allows for input of mathematical expressions using buttons for various functions such as exponentiation \( a^b \), sine function \( \sin(a) \), and alpha notation \( \alpha \).
**Task:**
\[ \cos \left( \frac{\pi}{12} \right) = \]
**Note:**
Show your work and explain, in your own words, how you arrived at your answer.
---
**Hints for Solving:**
You can use the identity for the cosine of a sum or difference:
\[
\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b
\]
Consider breaking down \( \frac{\pi}{12} \) using known angles like \( \frac{\pi}{6} \), \( \frac{\pi}{4} \), \( \frac{\pi}{3} \), etc.
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