## The Solutions To Sin(𝜃) = 1/2 Are: 𝜃 = 𝜋/6

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The equations sin(𝜃) = 1/2 result in the solutions: 𝜃 = 𝜋/6 + 2𝜋𝑘 or 𝜃 = 5𝜋/6 + 2𝜋𝑘, where 𝑘 is an integer.

To solve sin(3𝑥) = 1/2 within the interval [0, 2𝜋), we can use the solutions for sin(𝜃) = 1/2 and solve for 3𝑥 within this interval.

The solutions for sin(3𝑥) = 1/2 within the interval [0, 2𝜋) are: 3𝑥 = π/6 + 2π𝑘 or 3𝑥 = 5π/6 + 2π𝑘 where k is an integer.

We can then solve for 𝑥 by dividing both sides by 3: 𝑥 = π/18 + (2π𝑘)/3 or 𝑥 = 5π/18 + (2π𝑘)/3, where k is an integer and the solutions are within the interval [0, 2𝜋).

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