What are the operating signs of sine and cosine functions in Quadrant 4 of the unit circle?

What are the operating signs of sine and cosine functions in Quadrant 4 of the unit circle?

• A. Sine positive, Cosine positive
• B. Sine negative, Cosine positive
• C. Sine positive, Cosine negative
• D. Sine negative, Cosine negative

Answer: (A)

In Quadrant 4 of the unit circle, the sine function corresponds to the y-coordinate, while the cosine function corresponds to the x-coordinate of points on the circle. In this quadrant, the y-coordinates are negative, meaning the sine values are negative. Conversely, the x-coordinates are positive in this quadrant, indicating that the cosine values are positive. Thus, in Quadrant 4, sine takes on negative values, and cosine takes on positive values. This understanding of how the sine and cosine functions operate in different quadrants is crucial when analyzing trigonometric values and can be applied to various problems involving angles and their respective functions.

In Quadrant 4 of the unit circle, the sine function corresponds to the y-coordinate, while the cosine function corresponds to the x-coordinate of points on the circle. In this quadrant, the y-coordinates are negative, meaning the sine values are negative. Conversely, the x-coordinates are positive in this quadrant, indicating that the cosine values are positive.

Thus, in Quadrant 4, sine takes on negative values, and cosine takes on positive values. This understanding of how the sine and cosine functions operate in different quadrants is crucial when analyzing trigonometric values and can be applied to various problems involving angles and their respective functions.