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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Question
![**Problem Statement:**
Find the equation of the tangent line to the given function at the point where \( x = \frac{\pi}{2} \).
\[ y = \sin(\cos x) \]
**Explanation:**
This problem requires you to determine the equation of the tangent line to the function \( y = \sin(\cos x) \) at a specific point where \( x = \frac{\pi}{2} \). To solve this, you will need to:
1. Compute the derivative of the function to find the slope of the tangent line.
2. Evaluate this derivative at \( x = \frac{\pi}{2} \) to find the slope at the given point.
3. Use the point-slope form of a line equation to find the equation of the tangent line.
This involves applying calculus principles such as differentiation and understanding trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc4bd04-a070-4f0a-8c81-81114a590c8c%2F3d81fa7c-1e34-40f2-a9d5-8800fd2b7633%2Fz0d4ez_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the equation of the tangent line to the given function at the point where \( x = \frac{\pi}{2} \).
\[ y = \sin(\cos x) \]
**Explanation:**
This problem requires you to determine the equation of the tangent line to the function \( y = \sin(\cos x) \) at a specific point where \( x = \frac{\pi}{2} \). To solve this, you will need to:
1. Compute the derivative of the function to find the slope of the tangent line.
2. Evaluate this derivative at \( x = \frac{\pi}{2} \) to find the slope at the given point.
3. Use the point-slope form of a line equation to find the equation of the tangent line.
This involves applying calculus principles such as differentiation and understanding trigonometric functions.
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