Solve for x 2sin(x)-1=0

Problem

2*sin(x)−1=0

Solution

1. Isolate the sine term by adding 1 to both sides of the equation.

2*sin(x)=1

2. Divide both sides by 2 to solve for sin(x)

sin(x)=1/2

3. Identify the reference angle in the first quadrant where the sine value is 1/2

x=π/6

4. Determine all solutions within the standard interval [0,2*π) by finding where sine is positive (Quadrants I and II).

x=π/6

x=π−π/6=(5*π)/6

5. Generalize the solution by adding multiples of the period 2*π to account for all possible values of x

x=π/6+2*k*π

x=(5*π)/6+2*k*π

Final Answer

x=π/6+2*k*π,(5*π)/6+2*k*π

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