Find a positive angle less than 2piπ that is coterminal with the given angle.
StartFraction 11 pi Over 3 EndFraction
11π/3
To find a positive angle less than 2π that is coterminal with 11π/3, we need to subtract multiples of 2π from the given angle until we get an angle within the range of 0 ≤ θ < 2π.
First, let's simplify 11π/3 by dividing the number in the numerator by the number in the denominator:
11π/3 = 3.666...π
Since this angle is greater than 2π, we know it is already in the range of 0 ≤ θ < 2π. Therefore, 11π/3 is coterminal with itself in this case.
So, the positive angle less than 2π that is coterminal with 11π/3 is 11π/3 itself.
To find a positive angle that is coterminal with 11π/3, you can add or subtract any multiple of 2π.
First, let's convert 11π/3 to a mixed number. Divide 11 by 3:
11 ÷ 3 = 3 remainder 2
So, 11π/3 is equivalent to 3π + 2π/3.
Now, to find a positive coterminal angle, we add or subtract multiples of 2π:
3π + 2π/3 + 2π = 7π + 2π/3
This angle is coterminal with 11π/3 and is less than 2π.
each 2 π (radians) is a complete circle , and the angles keep repeating
11/3 π is 6/3 π for the full circle , and 5/3 π beyond