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

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

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3sin(θ)+3=2cos^2(θ)

3 sin (θ) + 3 = 2 cos^{2} (θ)

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

Solution steps

3 sin (θ) + 3 = 2 cos^{2} (θ)

Subtract

2 cos^{2} (θ)

from both sides

3 sin (θ) + 3 - 2 cos^{2} (θ) = 0

Rewrite using trig identities

1 + 2 sin^{2} (θ) + 3 sin (θ) = 0

Solve by substitution

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

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

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

Combine all the solutions

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

cos (x) = - \frac{5}{6}

2 sin (\frac{x}{2}) - 3 = 0

2 sin^{2} (θ) = sin (θ) + 1

2 sec^{2} (x) - 4 = 0

tan (a) = 3

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