Solve for x 2sin(3x)-1=0

Problem

2*sin(3*x)−1=0

Solution

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

2*sin(3*x)=1

sin(3*x)=1/2

2. Determine the general solutions for the angle 3*x where the sine value is 1/2

3*x=π/6+2*n*π

3*x=(5*π)/6+2*n*π

3. Solve for x by dividing all terms in both equations by 3.

x=π/18+(2*n*π)/3

x=(5*π)/18+(2*n*π)/3

Final Answer

x=π/18+(2*n*π)/3,(5*π)/18+(2*n*π)/3

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