Solve by Factoring 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 values of x that satisfy the sine function for the given ratio.

2. Determine the reference angle by finding the value in the first quadrant where the sine is √(,3)/2

3. Apply the unit circle properties to find all solutions within the standard interval [0,2*π) Since sine is positive in the first and second quadrants, the solutions are x=π/3 and x=π−π/3

4. Simplify the second quadrant solution to get x=(2*π)/3

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

Final Answer

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

Want more problems? Check here!