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

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

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2cos^2(θ)+3sin(θ)=0

2 cos^{2} (θ) + 3 sin (θ) = 0

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

Solution steps

2 cos^{2} (θ) + 3 sin (θ) = 0

Rewrite using trig identities

(1 - sin^{2} (θ)) \cdot 2 + 3 sin (θ) = 0

Solve by substitution

sin (θ) = - \frac{1}{2}, sin (θ) = 2

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

sin (θ) = 2 :

No Solution

Combine all the solutions

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

sin (2 θ) + 3 cos (θ) = 0

2 cot (x) + csc^{2} (x) = 0

2 cos^{2} (θ) + 3 cos (θ) + 4 = 3

2 sin (3 θ) cos (2 θ) - cos (2 θ) = 0

2 sec (x) + 1 = sec (x) + 3

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