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The smallest positive number for which tan(3z) = 1 is z = .The next larger such number is z =

The smallest positive number for which tan(3z) = 1 is z = .The next larger such number is z =

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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## Problem 10 The task is to find the smallest positive number \( x \) for which the equation \(\tan(3x) = 1\) holds true. Additionally, identify the next larger such number. ### Solution: - Determine the smallest positive number \( x \) such that \(\tan(3x) = 1\). - The next larger such number can be given as \( x \). **Hint:** Apply an inverse trigonometric function and use the periodicity of the tangent function to find the solution. ### Explanation: - **Inverse Trigonometric Function:** Find \( x \) by evaluating the inverse tangent function. - **Periodicity:** Utilize the periodicity of the tangent function, \( \tan(\theta) = \tan(\theta + n\pi) \) for integer \( n \), to identify subsequent solutions.
Transcribed Image Text:## Problem 10 The task is to find the smallest positive number \( x \) for which the equation \(\tan(3x) = 1\) holds true. Additionally, identify the next larger such number. ### Solution: - Determine the smallest positive number \( x \) such that \(\tan(3x) = 1\). - The next larger such number can be given as \( x \). **Hint:** Apply an inverse trigonometric function and use the periodicity of the tangent function to find the solution. ### Explanation: - **Inverse Trigonometric Function:** Find \( x \) by evaluating the inverse tangent function. - **Periodicity:** Utilize the periodicity of the tangent function, \( \tan(\theta) = \tan(\theta + n\pi) \) for integer \( n \), to identify subsequent solutions.
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