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:**
Use the given conditions to find the exact value of the expression.
\[
\cos a = \frac{24}{25}, \quad \sin a < 0, \quad \cos \left( a + \frac{5\pi}{6} \right)
\]
**Analysis:**
This problem involves finding the cosine of the sum of two angles given specific trigonometric conditions. The expression is evaluated using the angle sum identity:
\[
\cos(a + b) = \cos a \cos b - \sin a \sin b
\]
Given:
1. \(\cos a = \frac{24}{25}\)
2. \(\sin a < 0\)
\(\frac{5\pi}{6}\) is in the second quadrant where cosine is negative and sine is positive. The values of \(\cos \frac{5\pi}{6}\) and \(\sin \frac{5\pi}{6}\) are essential for solving the expression using the cosine angle sum formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8a12d91-0c9d-47ce-a889-3cf33af6d298%2F184b5b19-4ea0-4a95-9808-ac57a04b083b%2Fhqrpkw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use the given conditions to find the exact value of the expression.
\[
\cos a = \frac{24}{25}, \quad \sin a < 0, \quad \cos \left( a + \frac{5\pi}{6} \right)
\]
**Analysis:**
This problem involves finding the cosine of the sum of two angles given specific trigonometric conditions. The expression is evaluated using the angle sum identity:
\[
\cos(a + b) = \cos a \cos b - \sin a \sin b
\]
Given:
1. \(\cos a = \frac{24}{25}\)
2. \(\sin a < 0\)
\(\frac{5\pi}{6}\) is in the second quadrant where cosine is negative and sine is positive. The values of \(\cos \frac{5\pi}{6}\) and \(\sin \frac{5\pi}{6}\) are essential for solving the expression using the cosine angle sum formula.
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