Solve for x sin(3x)=1/2

Problem

sin(3*x)=1/2

Solution

1. Identify the general solutions for the sine function where the output is 1/2 The sine of an angle is 1/2 at π/6 and (5*π)/6 within the first rotation.

2. Set up the equations for the argument 3*x by including the periodic constant 2*π*n where n is any integer.

3*x=π/6+2*π*n

3*x=(5*π)/6+2*π*n

3. Isolate x by dividing every term in both equations by 3

x=π/18+(2*π*n)/3

x=(5*π)/18+(2*π*n)/3

Final Answer

x=π/18+(2*π*n)/3,(5*π)/18+(2*π*n)/3

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