Find all real numbers that satisfy the following equation 2

Find all real numbers that satisfy the following equation 2 sin (2x) = -1 Select the correct choice below and, if necessary, fill in the answer within your choice. A. The solution set is {x | k = + k pi or x = + k pi}, where it is any integer. (Use integers or fractions for any numbers in the expression use ascending order. Type at answer, using x needed.) B. The solution sets is {x|k = + 2k pi or x = + 2 k pi}, where k is any integer. (Use integers or fractions for any numbers in the expression. Use ascending order. Type an answer, using needed) C. There is no solution.

Solution

we have given 2sin(2x)=-1

sin(2x)=-1/2

2x=-pi/6

x=-pi/12

To find the second solution, subtract the solution from 2, to find a reference angle. Next, add this reference angle to pi to find the solution in the third quadrant.

2x=2pi+pi/6+pi =19pi/6

x=19pi/12

the period function is 2pi/|b| =2pi/2 =pi since sin(2x)=-1,b=2

The period of the sin(2x) function is pi so values will repeat every pi radians in both directions

x=-pi/12(+/-)kpi,x=19pi/12(+/-)kpi,k is any integer

answer is A

A) the soluction set {x| x=-pi/12(+/-)kpi or x=19pi/12(+/-)kpi}