The only value of the angles that could not be the value of the θ is determined as 240⁰.
If sinθ is given as [tex]\frac{\sqrt{3} }{2}[/tex], then the value of θ is determined as follows;
sinθ = √3/2
sinθ = 0.866
θ = sin⁻¹(0.866)
θ = 60⁰
When the angle is translated in radians, θ = π/3 = 180/3 = 60⁰
thus, θ = π/3
2(π/3) = 2(60) = 120⁰
using the following formula, we can obtain the rest;
θ = π/3 + 2πk
when k = 1;
θ = π/3 + 2π(1)
θ = 60 + 2(180)
θ = 420⁰
Thus, the only value of the angles that could not be the value of the θ is determined as 240⁰.
Learn more about translation of angles here: https://brainly.com/question/2679720
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