Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

If [tex]\(\cos \theta \ \textless \ 0\)[/tex] and [tex]\(\cot \theta \ \textgreater \ 0\)[/tex], then the terminal point determined by [tex]\(\theta\)[/tex] is in:

A. Quadrant 1
B. Quadrant 4
C. Quadrant 3
D. Quadrant 2

Sagot :

GinnyAnswer
To determine in which quadrant the terminal point determined by [tex]\(\theta\)[/tex] lies, we need to carefully consider the conditions given:

1. [tex]\(\cos \theta < 0\)[/tex]:
- The cosine function is negative in quadrants II and III.

2. [tex]\(\cot \theta > 0\)[/tex]:
- Cotangent is the reciprocal of the tangent function, [tex]\(\cot \theta = \frac{\cos \theta}{\sin \theta}\)[/tex].
- Cotangent is positive when both sine and cosine have the same sign:
- [tex]\(\sin \theta > 0\)[/tex] and [tex]\(\cos \theta > 0\)[/tex], which occurs in quadrant I (but this conflicts with [tex]\(\cos \theta < 0\)[/tex]).
- [tex]\(\sin \theta < 0\)[/tex] and [tex]\(\cos \theta < 0\)[/tex], which occurs in quadrant III.

Given that [tex]\(\cos \theta < 0\)[/tex] forces us to look in quadrants II or III, and [tex]\(\cot \theta > 0\)[/tex] indicates that sine and cosine must share the same sign, the only suitable quadrant satisfying both conditions is quadrant III.

Therefore, the terminal point determined by [tex]\(\theta\)[/tex] is in:

C. quadrant 3
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.