Question

Solve for exact solutions over the interval [0, 2pi] sin2x=-1/2, what is the solution set?

Answer 1

x= 7pi/12, 11pi/12, 19pi/12, 23pi/12

Explanation:

sin 2x =-1/2

since we deal with 2x, we will multiply the interval by 2 -> [0, 4pi]

now sin(1/2)=pi/6

using ASTC, the quadrants we want are T and C. so, we have solutions pi+pi/6=7pi/6 and 2pi-pi/6=11pi/6

next, we add 2pi again until we reach 4pi.

next are 19pi/6 and 23pi/6. we can stop now.

our solution set is all these divided by 2.

thus, our solution set is x=7pi/12, 11pi/12, 19pi/12, 23pi/12