The quadrant where all functions are negative is located in the lower left quadrant of the Cartesian plane. This quadrant is bounded by the x-axis and the y-axis, and all points in this quadrant have both negative x-coordinates and negative y-coordinates. The quadrant is often referred to as quadrant III or QIII.
Quadrant Where All Functions Are Negative
The fourth quadrant is the one where all the functions are negative. This means that the sine, cosine, tangent, cotangent, secant, and cosecant functions are all negative in this quadrant.
- The sine function is negative because the y-coordinates of all the points in this quadrant are negative.
- The cosine function is negative because the x-coordinates of all the points in this quadrant are negative.
- The tangent function is negative because it is the ratio of the sine function to the cosine function, and both of these functions are negative in this quadrant.
- The cotangent function is negative because it is the ratio of the cosine function to the sine function, and both of these functions are negative in this quadrant.
- The secant function is negative because it is the reciprocal of the cosine function, and the cosine function is negative in this quadrant.
- The cosecant function is negative because it is the reciprocal of the sine function, and the sine function is negative in this quadrant.
The following table shows the signs of all the trigonometric functions in each quadrant:
| Quadrant | Sine | Cosine | Tangent | Cotangent | Secant | Cosecant |
|---|---|---|---|---|---|---|
| I | + | + | + | + | + | + |
| II | + | – | – | – | – | + |
| III | – | – | + | + | – | – |
| IV | – | + | – | – | + | – |
Question 1:
What is the quadrant where all trigonometric functions are negative?
Answer:
Subject: Quadrant
Predicate: All trigonometric functions are negative
Object: Fourth quadrant
Question 2:
In which quadrant is the sine function always negative?
Answer:
Subject: Sine function
Attribute: Always negative
Value: Fourth quadrant
Question 3:
What is the quadrant where both the cosine and tangent functions are negative?
Answer:
Entity: Quadrant
Attribute: Cosine and tangent functions are negative
Value: Third quadrant
Well, there you have it folks! Now you know all about the mysterious quadrant where all functions are negative. Thanks for hanging out with me and learning something new today. If you enjoyed this little adventure, be sure to stick around for more mathy goodness in the future. I promise to keep it fun and easy to understand. Until next time, keep your calculators close and your pencils sharp!