Final answer:
In quadrant 2, the value of sec(b) is -2. The values of x, y, and r are x = -1/2, y = √(15/4), and r = 2. The value of angle b is 60 degrees.
Step-by-step explanation:
In quadrant 2, the value of sec(b) is -2. We know that sec(b) is the reciprocal of cos(b), so cos(b) is -1/2.
In quadrant 2, the cosine function is negative.
Therefore, we can conclude that the reference angle is 60 degrees.
The values of x, y, and r can be determined using the unit circle.
In quadrant 2, x is negative and y is positive. Since cos(b) = x/r, we have cos(b) = -1/2 and r = 2.
Using the Pythagorean Theorem, we can find the value of y, which is √(r² - x²) = √(2² - (-1/2)²) = √(4 - 1/4) = √(15/4).
Therefore, x = -1/2, y = √(15/4), and r = 2. The value of angle b is the reference angle in quadrant 2, which is 60 degrees.