89°F Write the following expression in terms sine or cose, and then simplify if possible. sec(-8) - tanesin Use the paperclip button below to attach files. *Student can enter max 2000 characters XDE BIU 2 Ω Q Search
89°F Write the following expression in terms sine or cose, and then simplify if possible. sec(-8) - tanesin Use the paperclip button below to attach files. *Student can enter max 2000 characters XDE BIU 2 Ω Q Search
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 6GP
Related questions
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![## Problem Statement:
**Write the following expression in terms sinθ or cosθ, and then simplify if possible:**
\[ \sec(-\theta) - \tan(8\sin\theta) \]
**Instructions:**
Use the paperclip button below to attach files.
---
- *Student can enter max 2000 characters*
### Diagram:
There are no graphs or diagrams provided with this problem statement.
### Notes:
1. **Secant Function (\( \sec \))**: The secant function is the reciprocal of the cosine function. Hence, \(\sec(-\theta) = \frac{1}{\cos(-\theta)}\). Using the property of the cosine function, \(\cos(-\theta) = \cos(\theta)\).
2. **Tangent Function (\( \tan \))**: The tangent function is defined as the ratio of the sine and cosine functions, i.e., \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).
3. Incorporate the above transformations to simplify the given expression.
### Simplified Expression:
\[ \sec(-\theta) - \tan(8\sin\theta) \]
Using identities:
\[ \sec(-\theta) = \sec(\theta) = \frac{1}{\cos(\theta)} \]
Thus,
\[ \frac{1}{\cos(\theta)} - \tan(8\sin\theta) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f02248d-9b04-4bf9-ba6b-18c74681389d%2F5f5ad28a-843f-4c1b-a8d4-0b77aac475a1%2Fnjfe88m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement:
**Write the following expression in terms sinθ or cosθ, and then simplify if possible:**
\[ \sec(-\theta) - \tan(8\sin\theta) \]
**Instructions:**
Use the paperclip button below to attach files.
---
- *Student can enter max 2000 characters*
### Diagram:
There are no graphs or diagrams provided with this problem statement.
### Notes:
1. **Secant Function (\( \sec \))**: The secant function is the reciprocal of the cosine function. Hence, \(\sec(-\theta) = \frac{1}{\cos(-\theta)}\). Using the property of the cosine function, \(\cos(-\theta) = \cos(\theta)\).
2. **Tangent Function (\( \tan \))**: The tangent function is defined as the ratio of the sine and cosine functions, i.e., \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).
3. Incorporate the above transformations to simplify the given expression.
### Simplified Expression:
\[ \sec(-\theta) - \tan(8\sin\theta) \]
Using identities:
\[ \sec(-\theta) = \sec(\theta) = \frac{1}{\cos(\theta)} \]
Thus,
\[ \frac{1}{\cos(\theta)} - \tan(8\sin\theta) \]
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