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2 and 3 Suppose that tan 0 <0

2 and 3 Suppose that tan 0 <0

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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Question
Suppose that \(\tan \theta = -\frac{2}{3}\) and \(\frac{\pi}{2} < \theta < \pi\). Find the exact values of \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). ### Diagram Explanation The image includes a mathematical task where the goal is to determine the exact trigonometric values for half of the given angle \(\theta\), specifically \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). #### Calculator Interface There’s a calculator interface shown with icons that suggest operations related to fractions, roots, and \(\pi\). A box labeled "Undefined" indicates that some operations might result in an undefined value. Below the problem, there are placeholders in blue boxes for students to input their answers for \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). This exercise focuses on using half-angle identities in trigonometry to fill in these values correctly.
Transcribed Image Text:Suppose that \(\tan \theta = -\frac{2}{3}\) and \(\frac{\pi}{2} < \theta < \pi\). Find the exact values of \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). ### Diagram Explanation The image includes a mathematical task where the goal is to determine the exact trigonometric values for half of the given angle \(\theta\), specifically \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). #### Calculator Interface There’s a calculator interface shown with icons that suggest operations related to fractions, roots, and \(\pi\). A box labeled "Undefined" indicates that some operations might result in an undefined value. Below the problem, there are placeholders in blue boxes for students to input their answers for \(\sin \frac{\theta}{2}\) and \(\tan \frac{\theta}{2}\). This exercise focuses on using half-angle identities in trigonometry to fill in these values correctly.
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