What is the general solution for 5sin(θ)+1=3sin(θ) ?

The general solution for 5sin(θ)+1=3sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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5sin(θ)+1=3sin(θ)

5 sin (θ) + 1 = 3 sin (θ)

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

Solution steps

5 sin (θ) + 1 = 3 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

sin (x) = 1 + cos (x)

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

sin (2 x) = 0.8

cot (x) = tan (x)

2 sin^{2} (x) + 3 = 0

What is the general solution for 5sin(θ)+1=3sin(θ) ?
The general solution for 5sin(θ)+1=3sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin