a Find all values of x in the interval 0 2 that satisfy the

a.) Find all values of x in the interval [0, 2] that satisfy the equation. (Enter your answers as a comma-separated list.)

12 sin2(x) = 6

b.) Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.)

12 cos(x) + 6 > 0

Solution

a)12 sin²(x) = 6

sin²(x) = 6/12

sin²(x) = 1/2

sin(x) = 1/2 ,sin(x)=-1/2

x=/4,3/4 ,5/4 ,7/4

if your question is 12 sin(2x) = 6

sin2x=6/12

sin2x=1/2

2x =/6,5/6,13/6,17/6

x =/12,5/12,13/12,17/12

b)12 cos(x) + 6 > 0

12 cos(x) > -6

cos(x) > -6/12

cos(x) > -1/2

x=[0,2/3)U(4/3,2]