Find an angle between o and 2pi that is coterminal with the given angle
-8pi/3:
71pi/2:
11pi/7:
To find an angle that is coterminal with a given angle, we need to add or subtract a multiple of 2π (or 360°) to the given angle. This is because coterminal angles have the same initial and terminal side when drawn in standard position on the coordinate plane.
Let's find an angle between 0 and 2π that is coterminal with each given angle:
1. -8π/3:
To find a positive coterminal angle, we need to add a multiple of 2π.
First, convert the angle to a mixed number: -8π/3 = -2⅔π.
To find a positive coterminal angle, we can add 2π to -8π/3.
-2⅔π + 2π = -⅔π.
Thus, an angle between 0 and 2π that is coterminal with -8π/3 is -⅔π.
2. 71π/2:
To find an angle between 0 and 2π that is coterminal with 71π/2, we can subtract multiple of 2π.
First, convert the angle to a mixed number: 71π/2 = 35½π.
To find an angle between 0 and 2π, we can subtract 2π from 35½π.
35½π - 2π = 33½π.
Thus, an angle between 0 and 2π that is coterminal with 71π/2 is 33½π.
3. 11π/7:
To find an angle between 0 and 2π that is coterminal with 11π/7, we can add or subtract multiples of 2π.
First, convert the angle to a mixed number: 11π/7.
To find a positive coterminal angle, we can add 2π to 11π/7.
11π/7 + 2π = 25π/7.
Thus, an angle between 0 and 2π that is coterminal with 11π/7 is 25π/7.
Keep in mind that there can be infinitely many coterminal angles as you continue adding or subtracting multiples of 2π.