Posted by Jade on .
find all values of theta in the interval 0<theta<360 that satisfy the equation 3cos 2theta + 2 sin theta+1=0

Trigonometry 
Reiny,
3cos^2 Ø + 2sinØ + 1 = 0
3(1  sin^2 Ø) + 2sinØ + 1 = 0
3sin^2Ø  2sinØ 4 = 0
sinØ = (2 ± √28)/6
= 1.215.. which is not admissable
or
sinØ = .54858...
so Ø is in III or IV
the angle in standard position is 33.27°
so Ø = 213.27° or Ø = 326.73°