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
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Question
![**Computation of Trigonometric Functions for Angle \( \beta = \frac{7\pi}{4} \) radians**
Given the angle \( \beta = \frac{7\pi}{4} \) radians, we can compute the six primary trigonometric functions (cosine, sine, tangent, cotangent, secant, and cosecant) for this angle.
1. **Cosine Function (\( \cos(\beta) \)):**
2. **Sine Function (\( \sin(\beta) \)):**
3. **Tangent Function (\( \tan(\beta) \)):**
4. **Cotangent Function (\( \cot(\beta) \)):**
5. **Secant Function (\( \sec(\beta) \)):**
6. **Cosecant Function (\( \csc(\beta) \)):**
Below are their respective placeholder expressions:
- \( \cos(\beta) = \)
- \( \sin(\beta) = \)
- \( \tan(\beta) = \)
- \( \cot(\beta) = \)
- \( \sec(\beta) = \)
- \( \csc(\beta) = \)
To compute these functions, we need to recognize that:
\[ \frac{7\pi}{4} = 2\pi - \frac{\pi}{4} \]
This angle is equivalent to the standard position angle \( -\frac{\pi}{4} \) or \( \frac{7\pi}{4} \) (which is in the fourth quadrant). Use the unit circle or trigonometric identities accordingly to find the exact values for these functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aee7c7d-285e-49c9-ad3b-faae5963cfad%2F7d7250a4-8e68-4243-89ed-bfc96214e54b%2Fbgazf5h_processed.png&w=3840&q=75)
Transcribed Image Text:**Computation of Trigonometric Functions for Angle \( \beta = \frac{7\pi}{4} \) radians**
Given the angle \( \beta = \frac{7\pi}{4} \) radians, we can compute the six primary trigonometric functions (cosine, sine, tangent, cotangent, secant, and cosecant) for this angle.
1. **Cosine Function (\( \cos(\beta) \)):**
2. **Sine Function (\( \sin(\beta) \)):**
3. **Tangent Function (\( \tan(\beta) \)):**
4. **Cotangent Function (\( \cot(\beta) \)):**
5. **Secant Function (\( \sec(\beta) \)):**
6. **Cosecant Function (\( \csc(\beta) \)):**
Below are their respective placeholder expressions:
- \( \cos(\beta) = \)
- \( \sin(\beta) = \)
- \( \tan(\beta) = \)
- \( \cot(\beta) = \)
- \( \sec(\beta) = \)
- \( \csc(\beta) = \)
To compute these functions, we need to recognize that:
\[ \frac{7\pi}{4} = 2\pi - \frac{\pi}{4} \]
This angle is equivalent to the standard position angle \( -\frac{\pi}{4} \) or \( \frac{7\pi}{4} \) (which is in the fourth quadrant). Use the unit circle or trigonometric identities accordingly to find the exact values for these functions.
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