Solve for x 2sin(x)=1

Problem

2*sin(x)=1

Solution

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

sin(x)=1/2

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

x=π/6

3. Determine the second solution within the interval [0,2*π) by using the property that sine is positive in the second quadrant.

x=π−π/6

x=(5*π)/6

4. Generalize the solution to include all possible values of x by adding multiples of the period 2*π where n is any integer.

x=π/6+2*n*π

x=(5*π)/6+2*n*π

Final Answer

x=π/6+2*n*π,(5*π)/6+2*n*π

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