In Quadrant 4, what is the sign of the sine function?

In Quadrant 4, what is the sign of the sine function?

• A. Positive
• B. Negative
• C. Zero
• D. Undefined

Answer: (B)

In Quadrant 4 of the Cartesian coordinate system, the sine function represents the y-coordinate of a point on the unit circle. In this quadrant, the x-coordinates are positive while the y-coordinates are negative. Since the sine function directly corresponds to the y-value, the sine of any angle whose terminal side is in the fourth quadrant will always be negative. This understanding of the unit circle is fundamental to trigonometric functions and their respective signs in each quadrant. Thus, because the sine values in Quadrant 4 are derived from negative y-coordinates, the correct answer—reflecting that sine is negative in this quadrant—accurately captures the behavior of the function.

In Quadrant 4 of the Cartesian coordinate system, the sine function represents the y-coordinate of a point on the unit circle. In this quadrant, the x-coordinates are positive while the y-coordinates are negative. Since the sine function directly corresponds to the y-value, the sine of any angle whose terminal side is in the fourth quadrant will always be negative. This understanding of the unit circle is fundamental to trigonometric functions and their respective signs in each quadrant.

Thus, because the sine values in Quadrant 4 are derived from negative y-coordinates, the correct answer—reflecting that sine is negative in this quadrant—accurately captures the behavior of the function.