Solve for θ in Radians sin(theta)=1/2

Problem

sin(θ)=1/2

Solution

1. Identify the reference angle in the first quadrant where the sine function equals 1/2

θ=π/6

2. Determine the second quadrant angle where the sine function is also positive.

θ=π−π/6

θ=(5*π)/6

3. Generalize the solution to account for the periodicity of the sine function, which repeats every 2*π radians.

θ=π/6+2*k*π

θ=(5*π)/6+2*k*π

4. Define the variable k as any integer.

k∈ℤ

Final Answer

θ=π/6+2*k*π,(5*π)/6+2*k*π

Want more problems? Check here!