As in Example 1c of Section 5.1, assume tan e = -2.7, and e is in the second quadrant. Use one of the fundamental identities to find cot(-0). Provide 4 decimal places. Answer:
As in Example 1c of Section 5.1, assume tan e = -2.7, and e is in the second quadrant. Use one of the fundamental identities to find cot(-0). Provide 4 decimal places. Answer:
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
The second image is Example 1.c. For reference
Transcribed Image Text:As in Example 1c of Section 5.1, assume \(\tan \theta = -2.7\), and \(\theta\) is in the second quadrant. Use one of the fundamental identities to find \(\cot(-\theta)\). Provide 4 decimal places.
**Answer:**
![The image contains a trigonometry exercise involving the manipulation of trigonometric identities. Below is a transcription with explanations:
### Trigonometric Identities and Calculations
- **Given:**
- \(\sin \theta = \frac{5 \sqrt{34}}{34}\)
- **Objective:**
- Use reciprocal identities to relate the tangent and cotangent functions.
#### Example Problem
- **Expression:**
\[
\cot(-\theta)
\]
- **Calculations:**
1. **Reciprocal Identity:**
\[
\cot(-\theta) = \frac{1}{\tan(-\theta)}
\]
2. **Even-Odd Identity:**
- \(\tan(-\theta) = -\tan(\theta)\)
3. **Substitute and Simplify:**
\[
= \frac{1}{-\tan(\theta)} = -\frac{1}{\tan(\theta)}
\]
4. **Further Simplification:**
\[
= -\left(\frac{1}{\frac{5}{3}}\right) = -\left(\frac{3}{5}\right)
\]
5. **Multiply and Rewrite:**
\[
= 1 \div \left(\frac{5}{3}\right) = 1 \cdot \frac{3}{5} = \frac{3}{5}
\]
#### Exercises
Now try solving these similar problems:
- **Exercises:**
- 11
- 19
- 31
This section demonstrates the application of reciprocal identities and even-odd identities associated with trigonometric functions to solve expressions involving cotangents and tangents. It is important to thoroughly understand these identities to simplify and solve trigonometric problems effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26a21d52-7816-4917-a16a-44de3883c3a3%2Fd8b45f53-d7cd-4ddc-89d1-2342c02bbf6b%2F82hpzgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a trigonometry exercise involving the manipulation of trigonometric identities. Below is a transcription with explanations:
### Trigonometric Identities and Calculations
- **Given:**
- \(\sin \theta = \frac{5 \sqrt{34}}{34}\)
- **Objective:**
- Use reciprocal identities to relate the tangent and cotangent functions.
#### Example Problem
- **Expression:**
\[
\cot(-\theta)
\]
- **Calculations:**
1. **Reciprocal Identity:**
\[
\cot(-\theta) = \frac{1}{\tan(-\theta)}
\]
2. **Even-Odd Identity:**
- \(\tan(-\theta) = -\tan(\theta)\)
3. **Substitute and Simplify:**
\[
= \frac{1}{-\tan(\theta)} = -\frac{1}{\tan(\theta)}
\]
4. **Further Simplification:**
\[
= -\left(\frac{1}{\frac{5}{3}}\right) = -\left(\frac{3}{5}\right)
\]
5. **Multiply and Rewrite:**
\[
= 1 \div \left(\frac{5}{3}\right) = 1 \cdot \frac{3}{5} = \frac{3}{5}
\]
#### Exercises
Now try solving these similar problems:
- **Exercises:**
- 11
- 19
- 31
This section demonstrates the application of reciprocal identities and even-odd identities associated with trigonometric functions to solve expressions involving cotangents and tangents. It is important to thoroughly understand these identities to simplify and solve trigonometric problems effectively.
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