Name the quadrant in which the angle e lies. cos 8>0, cot 0<0 Choose the correct answer below. O Quadrant IV O Quadrant II O Quadrant II O Quadrant I
Name the quadrant in which the angle e lies. cos 8>0, cot 0<0 Choose the correct answer below. O Quadrant IV O Quadrant II O Quadrant II O Quadrant I
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°.
Related questions
Question
![**Problem: Determine the Quadrant**
Name the quadrant in which the angle \( \theta \) lies.
Given:
\[ \cos \theta > 0, \cot \theta < 0 \]
Choose the correct answer below:
- ○ Quadrant IV
- ○ Quadrant II
- ○ Quadrant III
- ○ Quadrant I
**Explanation:**
In the Cartesian coordinate system, the four quadrants are defined as follows:
- **Quadrant I**: All trigonometric ratios are positive.
- **Quadrant II**: Sine is positive; cosine and tangent are negative.
- **Quadrant III**: Tangent is positive; sine and cosine are negative.
- **Quadrant IV**: Cosine is positive; sine and tangent are negative.
To find the correct quadrant for \( \theta \):
- \( \cos \theta > 0 \) indicates either Quadrant I or IV.
- \( \cot \theta < 0 \) (since \( \cot \theta = \frac{1}{\tan \theta} \)), the tangent is negative, which indicates Quadrant IV.
Thus, the angle \( \theta \) lies in **Quadrant IV**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72c2cbed-dcf9-4d9b-9c7c-d7c84e72018f%2F5a6173f5-ce46-4ad1-b06b-7dd702d88980%2Fg1uxkka_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Determine the Quadrant**
Name the quadrant in which the angle \( \theta \) lies.
Given:
\[ \cos \theta > 0, \cot \theta < 0 \]
Choose the correct answer below:
- ○ Quadrant IV
- ○ Quadrant II
- ○ Quadrant III
- ○ Quadrant I
**Explanation:**
In the Cartesian coordinate system, the four quadrants are defined as follows:
- **Quadrant I**: All trigonometric ratios are positive.
- **Quadrant II**: Sine is positive; cosine and tangent are negative.
- **Quadrant III**: Tangent is positive; sine and cosine are negative.
- **Quadrant IV**: Cosine is positive; sine and tangent are negative.
To find the correct quadrant for \( \theta \):
- \( \cos \theta > 0 \) indicates either Quadrant I or IV.
- \( \cot \theta < 0 \) (since \( \cot \theta = \frac{1}{\tan \theta} \)), the tangent is negative, which indicates Quadrant IV.
Thus, the angle \( \theta \) lies in **Quadrant IV**.
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