Find x and approximate to 4 decimal places 0 2pi sin2x3sinx3

Find x and approximate to 4 decimal places. [0, 2pi)

sin²x-3sinx-3=0

Solution

sin^2 x -3sinx -3=0

this is of the form

ax^2 +bx +c =0

roots are = 3 + sqrt(9 +12) / 2 and 3 - sqrt(9+12) / 2

roots are = 3 + sqrt(21) / 2 and 3 - sqrt(21) / 2

= (3 +4.6) /2 and 3 - 4.6)/2

=7.6/2 and -1.6/2

= 3.8 and -0.8

so sinx = 3.8 or sinx =-0.8

but sinx = 3.8 is not possible

so sinx =-0.8

x = arc sin(-0.8)

x = -53.130

x = 233.13 degree and 306.87