Find all real numbers that satisfy the equation sinx 12 Sel

Find all real numbers that satisfy the equation. sinx = -1/2 Select the correct answer below, and if necessary, fill in the answer box(es) to complete your choice. A. The solution set is {x | x = +2 pi k}, where k is any integer. (Type your answer in radians. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the ex B. The solution set is {x | x = + pi k}, where k is any integer. (Type your answer in radians. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the ex C. The solution set is {x | x = + 2 pi k or x = + 2 pi k}, where k is any integer. (Type your answer in radians. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression. Use ascending order.) There is no solution.

Solution

sin x= - 1/2

sin x = sin( - pi/ 6)

x= - pi/ 6

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also sin x = - 1/2

sin x = sin ( pi + pi/6)

x= 7 pi/ 6

ans- c

x= - pi/ 6 + 2*pi*k or x = 7 pi/ 6 + 2*pi*k k is any interger

[ we used 2*pi since period of sin x is 2 pi]