Question 3 Given A -4 cos(0)= and <0<π, what is the value of cos(20)? B C |- D 5 -8 | 5 25 16 25
Question 3 Given A -4 cos(0)= and <0<π, what is the value of cos(20)? B C |- D 5 -8 | 5 25 16 25
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
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![### Question 3
Given \(\cos(\theta) = -\frac{4}{5}\) and \(\frac{\pi}{2} < \theta < \pi\), what is the value of \(\cos(2\theta)\)?
#### Answer Choices:
- A. \(-\frac{21}{5}\)
- B. \(-\frac{8}{5}\)
- C. \(\frac{7}{25}\)
- D. \(\frac{16}{25}\)
Note: (Taken from an online mathematics quiz platform which shows it is question number 3 out of a total of 13 questions, with 4 already answered correctly.)
#### Solution Explanation:
1. Remember the double-angle formula for cosine:
\[
\cos(2\theta) = 2\cos^2(\theta) - 1
\]
2. Substitute \(\cos(\theta) = -\frac{4}{5}\):
\[
\cos^2(\theta) = \left(-\frac{4}{5}\right)^2 = \frac{16}{25}
\]
3. Then calculate:
\[
\cos(2\theta) = 2 \cdot \frac{16}{25} - 1 = \frac{32}{25} - 1 = \frac{32}{25} - \frac{25}{25} = \frac{7}{25}
\]
Thus, the correct answer is:
- C. \(\frac{7}{25}\)
#### Diagram/Graph Explanation:
There are no diagrams or graphs associated with this question.
(Note: The image depicts a computer screen showing a mathematics question on trigonometry from an online quiz platform. The question number, progress, and submitted answers are displayed on the screen, alongside the Windows taskbar with various open applications.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F075db94c-9df1-4bd0-8bd8-7247d457f29a%2F5b02337e-a5db-44d6-b9ad-908f7415ef8d%2F8ww2s6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 3
Given \(\cos(\theta) = -\frac{4}{5}\) and \(\frac{\pi}{2} < \theta < \pi\), what is the value of \(\cos(2\theta)\)?
#### Answer Choices:
- A. \(-\frac{21}{5}\)
- B. \(-\frac{8}{5}\)
- C. \(\frac{7}{25}\)
- D. \(\frac{16}{25}\)
Note: (Taken from an online mathematics quiz platform which shows it is question number 3 out of a total of 13 questions, with 4 already answered correctly.)
#### Solution Explanation:
1. Remember the double-angle formula for cosine:
\[
\cos(2\theta) = 2\cos^2(\theta) - 1
\]
2. Substitute \(\cos(\theta) = -\frac{4}{5}\):
\[
\cos^2(\theta) = \left(-\frac{4}{5}\right)^2 = \frac{16}{25}
\]
3. Then calculate:
\[
\cos(2\theta) = 2 \cdot \frac{16}{25} - 1 = \frac{32}{25} - 1 = \frac{32}{25} - \frac{25}{25} = \frac{7}{25}
\]
Thus, the correct answer is:
- C. \(\frac{7}{25}\)
#### Diagram/Graph Explanation:
There are no diagrams or graphs associated with this question.
(Note: The image depicts a computer screen showing a mathematics question on trigonometry from an online quiz platform. The question number, progress, and submitted answers are displayed on the screen, alongside the Windows taskbar with various open applications.)
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