find all solutions of the equation.\n\n\\( \\sin x = \\frac { \\sqrt { 3 } } { 2 } \\)\n\nselect the correct…

find all solutions of the equation.\n\n\\( \\sin x = \\frac { \\sqrt { 3 } } { 2 } \\)\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\n\\( \\bigcirc \\) a. \\( x = \\) \n\n(simplify your answer. type your answer(s) as an expression, using \\( n \\) as the variable, in the form \\( a + b n \\) where \\( 0 \\leq a < 2 \\pi \\). type any angle measures in radians, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\n\n\\( \\bigcirc \\) b. there is no solution.

find all solutions of the equation.\n\n\\( \\sin x = \\frac { \\sqrt { 3 } } { 2 } \\)\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\n\\( \\bigcirc \\) a. \\( x = \\) \n\n(simplify your answer. type your answer(s) as an expression, using \\( n \\) as the variable, in the form \\( a + b n \\) where \\( 0 \\leq a < 2 \\pi \\). type any angle measures in radians, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\n\n\\( \\bigcirc \\) b. there is no solution.

Answer

Explanation:

Step1: Recall the unit - circle values

We know that (\sin x=\frac{\sqrt{3}}{2}) when (x = \frac{\pi}{3}+ 2n\pi) (in the first - quadrant) and (x=\pi-\frac{\pi}{3}=\frac{2\pi}{3}+2n\pi) (in the second - quadrant) for (n\in\mathbb{Z}), because the sine function has a period of (2\pi).

Answer:

A. (x=\frac{\pi}{3}+2n\pi,\frac{2\pi}{3}+2n\pi)