find all exact solutions for 8sin^2 x=6 in interval x is greater than or equal to 0 and less than or equal to?

Question

2pi

Answer 1

Solve for x on [0,2π]

8sin² x = 6
sin² x = 6/8 = 3/4
sin x = ±(√3)/2

x = {π/3, 2π/3, 4π/3, 5π/3,}

Answer 2

8sin^2 x=6
sin^2 x=6/8=.75
sin x=+/-√3/2
x=arcsin +/-√3/2
x=+/-Π/3 in all quadrants
x=Π/3, 2Π/3, 4Π/3,5Π/3
x=-Π/3, -2Π/3, -4Π/3, -5Π/3

Answer 3

cos2t = 1 - 2sin^2t
8((1/2) - (1/2)cos(2x)) = 6
4(1 - cos(2x)) = 6
1 - cos(2x) = 6/4 = 3/2
cos(2x) = -3/2 + 1
cos(2x) = -1/2
2x = 2π/3, 4π/3, 8π/3, 10π/3, . . .
x = π/3, 2π/3, 4π/3, 5π/3

Answer 4

solutions are always of the form a + k2pi, where 0<=a<2pi
you can have more than one ''a

does this help ?

Answer 5

equal
the first sideis and the other side to you do the same to both side so u put and to and sub tract and 2 times 4 is 8

this is science