which angle is different than the rest

A. -4pi/3

B. -2pi/3

C. 2pi/3

D. 8pi/3

just start with -4pi/3 and start adding 2pi. You will run into two of the other three values. The remaining one is a different angle.

is the answer -2pi/3?

To determine which angle is different from the rest, we need to compare the given angles.

Let's convert all the angles to their equivalent values between 0 and 2π (or 0 to 360 degrees).
To do this, we'll use the fact that one full revolution is equal to 2π (or 360 degrees).

A. -4π/3:
To convert this angle to its equivalent positive angle, we add 2π to it:
-4π/3 + 2π = -4π/3 + 6π/3 = 2π/3
So, -4π/3 is equivalent to 2π/3.

B. -2π/3:
To convert this angle to its equivalent positive angle, we add 2π to it:
-2π/3 + 2π = -2π/3 + 6π/3 = 4π/3

C. 2π/3:
This angle is already between 0 and 2π/3.

D. 8π/3:
To convert this angle to its equivalent angle between 0 and 2π, we divide 8π/3 by 2π and consider the remainder:
8π/3 ÷ 2π = 4 with a remainder of 0. So, 8π/3 is equivalent to 0.

Now, we can compare the angles:
-4π/3 = 2π/3
-2π/3 ≠ 2π/3
2π/3 = 2π/3
8π/3 = 0

From the comparison, we see that -2π/3 is the only angle different from the rest. Therefore, the answer is B. -2π/3.