Which of the following is a solution to sin(x/2) = radical 3/2

Answer:sin ( x/ 2 )  =  - √ 3 /2 Take the inverse sine of both sides of the equation to extract  x from inside the sine. x/ 2 = arcsin ( − √ 3/ 2 ) The exact value of  arcsin ( − √ 3 /2 )  is  − π /3 . /x 2 = − π /3 Multiply both sides of the equation by  2 . 2 ⋅ x /2 = 2 ⋅ ( − π /3 ) Simplify both sides of the equation. x = − 2 π /3 The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from  2 π , to find a reference angle. Next, add this reference angle to  π  to find the solution in the third quadrant. x /2 = 2 π + π/ 3 + π Simplify the expression to find the second solution.  x = 2 π /3  4 π Add  4 π  to every negative angle to get positive angles.  x = 10 π /3 The period of the  sin ( x /2 )  function is  4 π  so values will repeat every  4 π  radians in both directions. x =2 π /3 + 4 π n , 10 π/ 3 + 4 π n , for any integer  n Exclude the solutions that do not make  sin ( x /2 ) = − √ 3/ 2  true. x = 10 π /3 + 4 π n , for any integer  n