What is the general solution for 2cos^2(θ)-3sin(θ)-3=0 ?

The general solution for 2cos^2(θ)-3sin(θ)-3=0 is θ=(3pi)/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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2cos^2(θ)-3sin(θ)-3=0

2 cos^{2} (θ) - 3 sin (θ) - 3 = 0

θ = \frac{3 π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

2 cos^{2} (θ) - 3 sin (θ) - 3 = 0

Rewrite using trig identities

- 1 - 2 sin^{2} (θ) - 3 sin (θ) = 0

Solve by substitution

sin (θ) = - 1, sin (θ) = - \frac{1}{2}

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sinh (x) = \frac{5}{12}, cosh (x)

sin (x) - cos^{2} (x) = sin^{2} (x)

cos^{4} (x) = 1 + sin^{4} (x)

- 4 cos^{2} (θ) - 11 cos (θ) - 1 = - 7 cos (θ)

0 = 1 + cos (\frac{x}{2})

What is the general solution for 2cos^2(θ)-3sin(θ)-3=0 ?
The general solution for 2cos^2(θ)-3sin(θ)-3=0 is θ=(3pi)/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin