Find the exact value of each of the remaining trigonometric functions of 8. Rationalize denominators when applicable. sec 8=-4, given that sin 8>0
Find the exact value of each of the remaining trigonometric functions of 8. Rationalize denominators when applicable. sec 8=-4, given that sin 8>0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section: Chapter Questions
Problem 5DE
Related questions
Question
![### Trigonometric Functions and Identities
#### Problem Statement:
Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable.
Given:
\[ \sec \theta = -4, \text{ given that } \sin \theta > 0 \]
---
#### Questions with Answer Choices:
**1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \sin \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**2. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \cos \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \tan \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**4. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \csc \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**5. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \cot \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
### Explanation:
Given the value of \( \sec \theta \) and the sign of \( \sin \theta \), determine the remaining trigonometric functions by leveraging trigonometric identities and relationships between the functions.
**Trigonometric Identities Recap:**
- \( \sec \theta = \frac{1}{\cos \theta} \)
- \( \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c3214b5-f2f5-4a89-904a-2906edf42c76%2F97f457c7-ef42-4be8-add6-d8127905d029%2F9y7sw97_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Functions and Identities
#### Problem Statement:
Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable.
Given:
\[ \sec \theta = -4, \text{ given that } \sin \theta > 0 \]
---
#### Questions with Answer Choices:
**1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \sin \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**2. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \cos \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \tan \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**4. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \csc \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
**5. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
(A) \( \cot \theta = \text{[ ]} \)
*(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)*
(B) The function is undefined.
---
### Explanation:
Given the value of \( \sec \theta \) and the sign of \( \sin \theta \), determine the remaining trigonometric functions by leveraging trigonometric identities and relationships between the functions.
**Trigonometric Identities Recap:**
- \( \sec \theta = \frac{1}{\cos \theta} \)
- \( \
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 3 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning