What is the equivalent principal argument of -2π/3 in the interval (0, 2π)?

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Multiple Choice

What is the equivalent principal argument of -2π/3 in the interval (0, 2π)?

Angles repeat every 2π, so adding or subtracting multiples of 2π gives the same direction. To place -2π/3 into the interval (0, 2π), add 2π: -2π/3 + 2π = 4π/3. This is 240 degrees, which lies between 0 and 2π, so it is the equivalent principal argument in that interval. The other options don’t lie in the interval or aren’t congruent to the original angle modulo 2π, so they aren’t the same direction.

Angles repeat every 2π, so adding or subtracting multiples of 2π gives the same direction. To place -2π/3 into the interval (0, 2π), add 2π: -2π/3 + 2π = 4π/3. This is 240 degrees, which lies between 0 and 2π, so it is the equivalent principal argument in that interval. The other options don’t lie in the interval or aren’t congruent to the original angle modulo 2π, so they aren’t the same direction.

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