Solve:
\[ \sin(2\theta) = \frac{1}{2} \]
Answer (3)
To solve the equation Sin(2θ) = 1/2, use the inverse sine function to find the values of θ in the unit circle that satisfy the equation. The solutions are** θ = /6 + 2n **and θ = 5/6 + 2n , where n is an integer. ;
2θ=sin^-1(0.5) Degrees: 2θ=30,150,390,510... θ=15,75,195,255...
Radians: 2θ=π/6,5π/6,13π/6,17π/6... θ=π/12,5π/12,13π/12,17π/12...
To solve sin ( 2 θ ) = 2 1 , we find that 2 θ = 3 0 ∘ and 15 0 ∘ in degrees, leading to general solutions for θ as 1 5 ∘ , 7 5 ∘ , 19 5 ∘ , and 25 5 ∘ . In radians, the solutions are 12 π , 12 5 π , 12 13 π , and 12 17 π . Both sets of solutions demonstrate the periodic nature of the sine function.
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