In Quadrant 2 of the unit circle, what is the operating sign of the cosine function?

In Quadrant 2 of the unit circle, what is the operating sign of the cosine function?

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

Answer: (B)

In Quadrant 2 of the unit circle, the cosine function represents the x-coordinate of points on the circle. In this quadrant, the x-coordinates of all points are negative, whereas the y-coordinates are positive. Since the cosine corresponds to the x-coordinate, it follows that the value of the cosine function in Quadrant 2 is negative. To visualize this further, consider a point on the unit circle in Quadrant 2, such as (−√2/2, √2/2). Here, the x-coordinate is −√2/2, which confirms that the cosine (the x-coordinate) is indeed negative. Therefore, in this quadrant, the operating sign of the cosine function is negative.

In Quadrant 2 of the unit circle, the cosine function represents the x-coordinate of points on the circle. In this quadrant, the x-coordinates of all points are negative, whereas the y-coordinates are positive. Since the cosine corresponds to the x-coordinate, it follows that the value of the cosine function in Quadrant 2 is negative.

To visualize this further, consider a point on the unit circle in Quadrant 2, such as (−√2/2, √2/2). Here, the x-coordinate is −√2/2, which confirms that the cosine (the x-coordinate) is indeed negative. Therefore, in this quadrant, the operating sign of the cosine function is negative.