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Find all values of t, -π/2 < t < π/2, for which the tangent line to the graph of x(t) = 4t + 3 tant, is horizontal. y(t) = 4t - 3 tan t,

Find all values of t, -π/2 < t < π/2, for which the tangent line to the graph of x(t) = 4t + 3 tant, is horizontal. y(t) = 4t - 3 tan t,

Calculus: Early Transcendentals
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 all values of \( t \), where \( -\pi/2 < t < \pi/2 \), for which the tangent line to the graph of \[ x(t) = 4t + 3\tan t, \quad y(t) = 4t - 3\tan t, \] is horizontal. --- **Options:** 1. No values of \( t \). 2. \( t = -\pi/4, \quad \pi/3 \).
Transcribed Image Text:**Problem Statement:** Find all values of \( t \), where \( -\pi/2 < t < \pi/2 \), for which the tangent line to the graph of \[ x(t) = 4t + 3\tan t, \quad y(t) = 4t - 3\tan t, \] is horizontal. --- **Options:** 1. No values of \( t \). 2. \( t = -\pi/4, \quad \pi/3 \).
3. \( t = -\frac{\pi}{3}, \frac{\pi}{6} \) 4. \( t = -\frac{\pi}{3}, \frac{\pi}{3} \) 5. \( t = -\frac{\pi}{6}, \frac{\pi}{6} \) 6. \( t = -\frac{\pi}{4}, \frac{\pi}{4} \) This text could serve as an example of solutions or values for a variable \( t \) in trigonometric contexts, such as angles in radians. Each pair of values represents possible solutions to an equation or situation where \( t \) could equal either value within each line.
Transcribed Image Text:3. \( t = -\frac{\pi}{3}, \frac{\pi}{6} \) 4. \( t = -\frac{\pi}{3}, \frac{\pi}{3} \) 5. \( t = -\frac{\pi}{6}, \frac{\pi}{6} \) 6. \( t = -\frac{\pi}{4}, \frac{\pi}{4} \) This text could serve as an example of solutions or values for a variable \( t \) in trigonometric contexts, such as angles in radians. Each pair of values represents possible solutions to an equation or situation where \( t \) could equal either value within each line.
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