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

Problem

sin(x)=√(,3)/2

Solution

1. Identify the equation as a basic trigonometric equation where we need to find the angle x whose sine value is √(,3)/2

2. Determine the reference angle in the first quadrant. From the unit circle, we know that sin(π/3)=√(,3)/2 (or 60.

3. Find the second solution within the interval [0,2*π) Since the sine function is positive in the second quadrant, we calculate x=π−π/3=(2*π)/3 (or 120.

4. Generalize the solution to account for the periodicity of the sine function, which repeats every 2*π radians. We add 2*n*π to each primary solution, where n is any integer.

Final Answer

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

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