Solve for x sin(x)=1/2

Problem

sin(x)=1/2

Solution

1. Identify the reference angle in the first quadrant where the sine function equals 1/2

sin(π/6)=1/2

2. Determine the quadrants where the sine function is positive. Sine is positive in Quadrant I and Quadrant II.

(x_1)=π/6

(x_2)=π−π/6=(5*π)/6

3. Generalize the solution to include all possible rotations by adding multiples of 2*π where n is any integer.

x=π/6+2*n*π

x=(5*π)/6+2*n*π

Final Answer

sin(x)=1/2⇒x=π/6+2*n*π,(5*π)/6+2*n*π

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