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

Problem

sin(x)=√(,2)/2

Solution

1. Identify the reference angle 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. Since √(,2)/2 is positive, x must be in Quadrant I or Quadrant II.

Quadrant I:x=π/4

Quadrant II:x=π−π/4=(3*π)/4

3. Generalize the solution to include all possible angles by adding multiples of the period of the sine function, which is 2*π

x=π/4+2*k*π

x=(3*π)/4+2*k*π

4. Define the variable k as any integer.

k∈ℤ

Final Answer

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

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