Question

find all values of theta in the interval 0<theta<360 that satisfy the equation 3cos 2theta + 2 sin theta+1=0
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°

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