What is the general solution for 6sin(θ)+1=4sin(θ) ?

The general solution for 6sin(θ)+1=4sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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6sin(θ)+1=4sin(θ)

6 sin (θ) + 1 = 4 sin (θ)

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

Solution steps

6 sin (θ) + 1 = 4 sin (θ)

Solve by substitution

sin (θ) = - \frac{1}{2}

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

tan (t) = - \frac{1}{3}

0 = 2 cos (θ) sin (θ) + cos (θ)

sin (x) = \frac{1}{2} tan (x)

8 (1 - cos (θ)) = sin^{2} (θ)

x, cos (x) = sin (x)

What is the general solution for 6sin(θ)+1=4sin(θ) ?
The general solution for 6sin(θ)+1=4sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin