Answer:
Explanation:
To find sin(alpha-beta), we can use the trigonometric identity:
sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)
We are given that sin(alpha) = 11/12 in the second quadrant and cos(beta) = 15/17 in the fourth quadrant. We can use the Pythagorean theorem to find sin(beta):
sin^2(beta) + cos^2(beta) = 1
sin(beta) = sqrt(1 - cos^2(beta))
sin(beta) = sqrt(1 - (15/17)^2)
sin(beta) = sqrt(1 - 225/289)
sin(beta) = sqrt(64/289)
sin(beta) = 8/17 (since sin(beta) is positive in the fourth quadrant)
Now we can plug in the values we know into the identity:
sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)
sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)
We still need to find cos(alpha), which we can do using the Pythagorean identity:
sin^2(alpha) + cos^2(alpha) = 1
cos(alpha) = sqrt(1 - sin^2(alpha))
cos(alpha) = sqrt(1 - (11/12)^2)
cos(alpha) = sqrt(23/144)
Now we can substitute this value into the expression for sin(alpha - beta):
sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)
sin(alpha - beta) = (11/12)(15/17) - sqrt(23/144)(8/17)
sin(alpha - beta) ≈ 0.210
Therefore, sin(alpha - beta) is approximately equal to 0.210.