By the concept of coterminal angles, a positive angle that is less than 2π radians and coterminal with the angle -37π/6 radians is the positive angle 11π/6 radians.
How to determine a coterminal angle
Two angles are coterminal when the two semirrays have the same direction, two consecutive coterminal angles have a difference of 2π radians. Then, we can determine the family of angles coterminal to a given angle:
θ' = θ + 2π · i, i ∈ [tex]\mathbb{Z}_{O}[/tex] (1)
Where i is the index of the coterminal angle.
If we know that θ = -37π/6 and i = 4, then the positive angle that is coterminal and less than 2π is:
θ' = -37π/6 + 2π · 4
θ' = 11π/6 rad
By the concept of coterminal angles, a positive angle that is less than 2π radians and coterminal with the angle -37π/6 radians is the positive angle 11π/6 radians.
To learn more on coterminal angles: https://brainly.com/question/23093580
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