What is the general solution for 10sin(θ)+1=3-2sin(θ) ?

The general solution for 10sin(θ)+1=3-2sin(θ) is θ=0.16744…+2pin,θ=pi-0.16744…+2pin

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10sin(θ)+1=3-2sin(θ)

10 sin (θ) + 1 = 3 - 2 sin (θ)

θ = 0.16744 \dots + 2 πn, θ = π - 0.16744 \dots + 2 πn

Solution steps

10 sin (θ) + 1 = 3 - 2 sin (θ)

Solve by substitution

sin (θ) = \frac{1}{6}

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

Combine all the solutions

θ = arcsin (\frac{1}{6}) + 2 πn, θ = π - arcsin (\frac{1}{6}) + 2 πn

Show solutions in decimal form

θ = 0.16744 \dots + 2 πn, θ = π - 0.16744 \dots + 2 πn

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

5 sin^{2} (x) + 3 sin (x) = 1

8 cos^{2} (x) - 16 cos (x) + 8 = 0

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

cos (2 θ) + 10 sin^{2} (θ) = 3

What is the general solution for 10sin(θ)+1=3-2sin(θ) ?
The general solution for 10sin(θ)+1=3-2sin(θ) is θ=0.16744…+2pin,θ=pi-0.16744…+2pin