Find the exact value of the trigonometric function of using the given format: 5п Let then is in Q (which quadrant?). Thus, tan is positive or negative (choose one). 57 If 0 then the reference angle =_____. Thus, tan = Therefore, tan
Find the exact value of the trigonometric function of using the given format: 5п Let then is in Q (which quadrant?). Thus, tan is positive or negative (choose one). 57 If 0 then the reference angle =_____. Thus, tan = Therefore, tan
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Example Problem on Trigonometric Functions
**Objective:**
Find the exact value of the trigonometric function of \( \theta \) using the given format.
**Problem Statement:**
Given:
\[ \theta = -\frac{5\pi}{6} \]
Determine the quadrant of \( \theta \):
\[ \theta \) is in \( Q___ \) (which quadrant?). Thus, \( \tan \theta \) is positive or negative (choose one).
Next, find the reference angle:
If
\[ \theta = -\frac{5\pi}{6} \]
then the reference angle \( \bar{\theta} = ___ \). Thus, \( \tan \bar{\theta} = \_\_\_\_\_\_
Therefore,
\[ \tan \theta = \_\_\_\_\_\_
**Explanation:**
1. **Quadrant Information:**
- Analyze the given angle \( \theta = -\frac{5\pi}{6} \).
- Determine which quadrant \( \theta \) lies in.
2. **Reference Angle Calculation:**
- Calculate the corresponding reference angle \( \bar{\theta} \) for \( \theta = -\frac{5\pi}{6} \).
- Determine the value of \( \tan \bar{\theta} \).
3. **Determine the Exact Value:**
- Using the information about the quadrant and reference angle, find the exact value of \( \tan \theta \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe2257a7-ec8b-4cb2-8972-c13e17aa7768%2Fbc09b86d-d7f4-4167-9509-646d13a1acb5%2F2jzhup4_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem on Trigonometric Functions
**Objective:**
Find the exact value of the trigonometric function of \( \theta \) using the given format.
**Problem Statement:**
Given:
\[ \theta = -\frac{5\pi}{6} \]
Determine the quadrant of \( \theta \):
\[ \theta \) is in \( Q___ \) (which quadrant?). Thus, \( \tan \theta \) is positive or negative (choose one).
Next, find the reference angle:
If
\[ \theta = -\frac{5\pi}{6} \]
then the reference angle \( \bar{\theta} = ___ \). Thus, \( \tan \bar{\theta} = \_\_\_\_\_\_
Therefore,
\[ \tan \theta = \_\_\_\_\_\_
**Explanation:**
1. **Quadrant Information:**
- Analyze the given angle \( \theta = -\frac{5\pi}{6} \).
- Determine which quadrant \( \theta \) lies in.
2. **Reference Angle Calculation:**
- Calculate the corresponding reference angle \( \bar{\theta} \) for \( \theta = -\frac{5\pi}{6} \).
- Determine the value of \( \tan \bar{\theta} \).
3. **Determine the Exact Value:**
- Using the information about the quadrant and reference angle, find the exact value of \( \tan \theta \).
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