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

Problem

cos(3*x)=1/2

Solution

1. Identify the general solutions for the cosine function where the output is 1/2

2. Apply the formula for the reference angles on the unit circle, which are π/3 and −π/3 (or (5*π)/3.

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

3*x=π/3+2*k*π

3*x=−π/3+2*k*π

4. Solve for x by dividing every term in both equations by 3

x=π/9+(2*k*π)/3

x=−π/9+(2*k*π)/3

Final Answer

cos(3*x)=1/2⇒x=±π/9+(2*k*π)/3

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