Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Trigonometry Problem: Finding cos 2θ
**Problem Statement:**
Given that \(90^\circ < \theta < 180^\circ\) and \(\cos \theta = -\frac{3}{5}\), find \(\cos 2\theta\).
**Multiple Choice Answers:**
- A) \(\frac{7}{25}\)
- B) \(-\frac{16}{25}\)
- C) \(-\frac{7}{25}\)
- D) \(\frac{16}{25}\)
**Explanation:**
To find \(\cos 2\theta\), you can use the double-angle identity for cosine:
\[
\cos 2\theta = 2\cos^2 \theta - 1
\]
First, calculate \( \cos^2 \theta \):
\[
\cos \theta = -\frac{3}{5}
\]
\[
\cos^2 \theta = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}
\]
Next, apply the value to the double-angle formula:
\[
\cos 2\theta = 2\left(\frac{9}{25}\right) - 1 = \frac{18}{25} - 1 = \frac{18}{25} - \frac{25}{25} = -\frac{7}{25}
\]
Thus, the correct answer is:
- C) \(-\frac{7}{25}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe20fc6e6-2ea7-4c1e-8366-712724b6961a%2F626881f5-6956-44c4-8b0d-41a15e96ac21%2Fzkxu4l_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem: Finding cos 2θ
**Problem Statement:**
Given that \(90^\circ < \theta < 180^\circ\) and \(\cos \theta = -\frac{3}{5}\), find \(\cos 2\theta\).
**Multiple Choice Answers:**
- A) \(\frac{7}{25}\)
- B) \(-\frac{16}{25}\)
- C) \(-\frac{7}{25}\)
- D) \(\frac{16}{25}\)
**Explanation:**
To find \(\cos 2\theta\), you can use the double-angle identity for cosine:
\[
\cos 2\theta = 2\cos^2 \theta - 1
\]
First, calculate \( \cos^2 \theta \):
\[
\cos \theta = -\frac{3}{5}
\]
\[
\cos^2 \theta = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}
\]
Next, apply the value to the double-angle formula:
\[
\cos 2\theta = 2\left(\frac{9}{25}\right) - 1 = \frac{18}{25} - 1 = \frac{18}{25} - \frac{25}{25} = -\frac{7}{25}
\]
Thus, the correct answer is:
- C) \(-\frac{7}{25}\)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education