Solve for x 2cos(3x)=1

Problem

2*cos(3*x)=1

Solution

1. Isolate the trigonometric function by dividing both sides of the equation by 2

cos(3*x)=1/2

2. Determine the general solutions for the angle 3*x by identifying where the cosine function equals 1/2 on the unit circle.

3*x=π/3+2*π*n

3*x=−π/3+2*π*n

3. Solve for x by dividing the entire expression by 3

x=π/9+(2*π*n)/3

x=−π/9+(2*π*n)/3

4. Define the variable n as any integer to represent all possible solutions.

n∈ℤ

Final Answer

x=±π/9+(2*π*n)/3

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