How do I find all angles, 0≤theta<360, that satisfy the equation below, to the nearest tenth of a degree: 8cos^2theta+6cos theta+6= 8cos theta+9?

Answer 1

write the equation as 8cos²θ +6cosθ +6 = 8cosθ +9 and simplify to get 8cos²θ -2cosθ -3 =0 now use the quadratic formula cosθ = ( 2 ±√(4 + 96))/16 and solve for the roots which gives cosθ = 12/16, -8/16 which is the same as cosθ =3/4 ,-1/2. The angles corresponding to these values are θ = 41.4, 318.6 , 120.