Solve for x sin(3x)=( square root of 3)/2

Problem

sin(3*x)=√(,3)/2

Solution

1. Identify the general solutions for the sine function where the value is √(,3)/2

2. Determine the reference angles on the unit circle, which are π/3 and (2*π)/3

3. Set up the equations for the argument 3*x including the period 2*k*π where k is any integer.

3*x=π/3+2*k*π

3*x=(2*π)/3+2*k*π

4. Isolate x by dividing both sides of each equation by 3

x=π/9+(2*k*π)/3

x=(2*π)/9+(2*k*π)/3

Final Answer

x=π/9+(2*k*π)/3,(2*π)/9+(2*k*π)/3

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