Determine two coterminal angles for 2pi/3
To determine two coterminal angles for 2π/3, we need to find angles that have the same initial side and terminal side as 2π/3 but differ by a multiple of 2π.
Coterminal angles can be found by adding or subtracting a full revolution of 2π (360 degrees) until we reach a desired angle while keeping the initial side and terminal side the same.
Let's find two positive coterminal angles for 2π/3:
1. First, add a full revolution (2π) to 2π/3:
2π/3 + 2π = 6π/3 + 6π/3 = 8π/3
2. The angle 8π/3 is one coterminal angle for 2π/3.
3. Now, to find another coterminal angle, subtract a full revolution (2π) from 2π/3:
2π/3 - 2π = 6π/3 - 6π/3 = 4π/3
4. The angle 4π/3 is another coterminal angle for 2π/3.
Therefore, two coterminal angles for 2π/3 are 8π/3 and 4π/3.
2π/3 + 2π*k
so pick any integer values for k