Solve for x sin(x)=( square root of 2)/2

Problem

sin(x)=√(,2)/2

Solution

1. Identify the reference angle by finding the value in the first quadrant where the sine function equals √(,2)/2

sin(π/4)=√(,2)/2

2. Determine the quadrants where the sine function is positive, which are Quadrant I and Quadrant II.

x=π/4

x=π−π/4=(3*π)/4

3. Generalize the solution by adding the period of the sine function, 2*π*n where n is any integer, to account for all possible rotations.

x=π/4+2*π*n

x=(3*π)/4+2*π*n

Final Answer

sin(x)=√(,2)/2⇒x=π/4+2*π*n,(3*π)/4+2*π*n

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