If sin A = with A in QII, find Cos 9 cos Cos COS Cos Cos 스2
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°.
Related questions
Question
![### Problem Statement
Given:
If \( \sin A = -\frac{4}{5} \) with \( A \) in the third quadrant (QIII), find \( \cos \frac{A}{2} \).
### Options
- \( \cos \frac{A}{2} = -\frac{9}{\sqrt{10}} \)
- \( \cos \frac{A}{2} = -\frac{1}{\sqrt{4}} \)
- \( \cos \frac{A}{2} = -\frac{1}{\sqrt{5}} \)
- \( \cos \frac{A}{2} = \frac{1}{\sqrt{9}} \)
- \( \cos \frac{A}{2} = \frac{1}{\sqrt{5}} \)
### Notes for Solving
To solve this problem, consider using the identity:
\[
\cos \frac{A}{2} = \pm \sqrt{\frac{1 + \cos A}{2}}
\]
Given that \( A \) is in the third quadrant, both sine and cosine are negative, thus helping determine the sign of the half-angle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd68e50e-a892-48f7-97fc-be1863a7761b%2F2563625d-9820-479e-90c0-db0d3efee7a7%2Ff04zmwp_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Given:
If \( \sin A = -\frac{4}{5} \) with \( A \) in the third quadrant (QIII), find \( \cos \frac{A}{2} \).
### Options
- \( \cos \frac{A}{2} = -\frac{9}{\sqrt{10}} \)
- \( \cos \frac{A}{2} = -\frac{1}{\sqrt{4}} \)
- \( \cos \frac{A}{2} = -\frac{1}{\sqrt{5}} \)
- \( \cos \frac{A}{2} = \frac{1}{\sqrt{9}} \)
- \( \cos \frac{A}{2} = \frac{1}{\sqrt{5}} \)
### Notes for Solving
To solve this problem, consider using the identity:
\[
\cos \frac{A}{2} = \pm \sqrt{\frac{1 + \cos A}{2}}
\]
Given that \( A \) is in the third quadrant, both sine and cosine are negative, thus helping determine the sign of the half-angle.
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