Evaluate.

1. sin^-1(-1/2)
2. cos^-1[(-root 3)/2]
3. arctan[(root3)/3]
4. cos(arccos2/3)
5. arcsin(sin 2pi)
6. sin(arccos 1)

I will be happy to critique your thinking or work.

I got these values as my answers:

1. -pi/6
2. 5pi/6
3. pi/6
4. 2/3
5. 2pi
6. 0

Sure! Let's evaluate each of these expressions step-by-step:

1. To evaluate sin^(-1)(-1/2), we need to find the angle whose sine is -1/2. The angle that satisfies this condition is -30 degrees or -π/6 radians. Therefore, sin^(-1)(-1/2) = -30 degrees or -π/6 radians.

2. To evaluate cos^(-1)[(-√3)/2], we need to find the angle whose cosine is (-√3)/2. The angle that satisfies this condition is 150 degrees or 5π/6 radians. Therefore, cos^(-1)[(-√3)/2] = 150 degrees or 5π/6 radians.

3. To evaluate arctan[(√3)/3], we need to find the angle whose tangent is (√3)/3. The angle that satisfies this condition is 30 degrees or π/6 radians. Therefore, arctan[(√3)/3] = 30 degrees or π/6 radians.

4. To evaluate cos(arccos(2/3)), we need to find the cosine of the angle whose cosine is 2/3. The angle that satisfies this condition is 48.19 degrees or 0.84 radians. Therefore, cos(arccos(2/3)) = cos(48.19 degrees) or cos(0.84 radians).

5. To evaluate arcsin(sin(2π)), we need to find the angle whose sine is sin(2π). The sine of any multiple of 2π is always 0. Therefore, arcsin(sin(2π)) = arcsin(0) = 0 degrees or 0 radians.

6. To evaluate sin(arccos(1)), we need to find the sine of the angle whose cosine is 1. The angle that satisfies this condition is 0 degrees or 0 radians. Therefore, sin(arccos(1)) = sin(0 degrees) or sin(0 radians).

Note: For the answers given in degrees, the radian equivalents are also mentioned. Also, be sure to double-check the units (degrees or radians) used in the context of the problem at hand.