Solve for x 2sin(2x)-1=0

Problem

2*sin(2*x)−1=0

Solution

1. Isolate the sine function by adding 1 to both sides and then dividing by 2.

2*sin(2*x)=1

sin(2*x)=1/2

2. Identify the reference angle for which the sine is 1/2

sin(θ)=1/2⇒θ=π/6

3. Determine the general solutions for the argument 2*x within one period [0,2*π) Sine is positive in the first and second quadrants.

2*x=π/6+2*k*π

2*x=(5*π)/6+2*k*π

4. Solve for x by dividing all terms by 2, where k is any integer.

x=π/12+k*π

x=(5*π)/12+k*π

Final Answer

x=π/12+k*π,(5*π)/12+k*π

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