Solve for x sin(x)=( square root of 3)/2

Problem

sin(x)=√(,3)/2

Solution

1. Identify the reference angle in the first quadrant where the sine function equals √(,3)/2

sin(π/3)=√(,3)/2

2. Determine the quadrants where the sine function is positive. Since √(,3)/2 is positive, x must terminate in Quadrant I or Quadrant II.

Quadrant I:x=π/3

Quadrant II:x=π−π/3=(2*π)/3

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

x=π/3+2*k*π

x=(2*π)/3+2*k*π

4. Define the variable k as any integer.

k∈ℤ

Final Answer

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

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