Solve for x sin(3x)=1

Problem

sin(3*x)=1

Solution

1. Identify the general solution for the sine function where the output is 1. The sine of an angle is 1 when the angle is π/2 plus any integer multiple of 2*π

sin(θ)=1⇒θ=π/2+2*n*π

2. Substitute the argument of the sine function, which is 3*x into the general solution formula.

3*x=π/2+2*n*π

3. Isolate the variable x by dividing both sides of the equation by 3.

x=(π/2+2*n*π)/3

4. Simplify the expression to find the final general solution for x where n represents any integer.

x=π/6+(2*n*π)/3

Final Answer

sin(3*x)=1⇒x=π/6+(2*n*π)/3

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