What are the operating signs of the sine function in Quadrant 2 of the unit circle?

What are the operating signs of the sine function in Quadrant 2 of the unit circle?

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

Answer: (A)

In Quadrant 2 of the unit circle, the sine function is indeed positive. To understand why, it’s important to know how the unit circle is structured. The unit circle is divided into four quadrants, with the first quadrant (Quadrant I) having both sine and cosine values as positive. In Quadrant II, while the cosine function becomes negative due to the x-coordinates of points being negative, the y-coordinates, which represent the sine values, remain positive. The sine of an angle is defined as the y-coordinate of the point on the unit circle corresponding to that angle. As the angle moves from 90 degrees (or \( \frac{\pi}{2} \) radians, where sine is 1) to 180 degrees (or \( \pi \) radians), the y-coordinate decreases from 1 to 0, but it stays positive throughout this interval. Thus, whenever you measure angles in Quadrant II, the sine values will always yield positive results. This understanding of the unit circle and the characteristics of sine in each quadrant clarifies why the correct answer is that sine is positive in Quadrant 2.

In Quadrant 2 of the unit circle, the sine function is indeed positive. To understand why, it’s important to know how the unit circle is structured. The unit circle is divided into four quadrants, with the first quadrant (Quadrant I) having both sine and cosine values as positive. In Quadrant II, while the cosine function becomes negative due to the x-coordinates of points being negative, the y-coordinates, which represent the sine values, remain positive.

The sine of an angle is defined as the y-coordinate of the point on the unit circle corresponding to that angle. As the angle moves from 90 degrees (or ( \frac{\pi}{2} ) radians, where sine is 1) to 180 degrees (or ( \pi ) radians), the y-coordinate decreases from 1 to 0, but it stays positive throughout this interval. Thus, whenever you measure angles in Quadrant II, the sine values will always yield positive results.

This understanding of the unit circle and the characteristics of sine in each quadrant clarifies why the correct answer is that sine is positive in Quadrant 2.