To solve the expression 2arcsin(-1/2) - 3arccos(√3/2), we first need to find the values of arcsin(-1/2) and arccos(√3/2).
arcsin(-1/2) is the angle whose sine is -1/2. The reference angle for this is π/6 (30 degrees) in the second quadrant. Since sine is negative in the third and fourth quadrants, the angle in which sine is -1/2 is 7π/6 (210 degrees).
arccos(√3/2) is the angle whose cosine is √3/2. The reference angle for this is π/6 (30 degrees) in the first quadrant. Therefore, the angle in which cosine is √3/2 is π/6 (30 degrees).
Now, we can substitute these values into the expression:
2(7π/6) - 3(π/6) = 14π/6 - 3π/6 = 11π/6
Therefore, the solution to the expression 2arcsin(-1/2) - 3arccos(√3/2) is 11π/6.
To solve the expression 2arcsin(-1/2) - 3arccos(√3/2), we first need to find the values of arcsin(-1/2) and arccos(√3/2).
arcsin(-1/2) is the angle whose sine is -1/2. The reference angle for this is π/6 (30 degrees) in the second quadrant. Since sine is negative in the third and fourth quadrants, the angle in which sine is -1/2 is 7π/6 (210 degrees).
arccos(√3/2) is the angle whose cosine is √3/2. The reference angle for this is π/6 (30 degrees) in the first quadrant. Therefore, the angle in which cosine is √3/2 is π/6 (30 degrees).
Now, we can substitute these values into the expression:
2(7π/6) - 3(π/6)
= 14π/6 - 3π/6
= 11π/6
Therefore, the solution to the expression 2arcsin(-1/2) - 3arccos(√3/2) is 11π/6.