What is the general solution for 9sin^2(θ)+19sin(θ)+8=7sin(θ)+4 ?

The general solution for 9sin^2(θ)+19sin(θ)+8=7sin(θ)+4 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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9sin^2(θ)+19sin(θ)+8=7sin(θ)+4

9 sin^{2} (θ) + 19 sin (θ) + 8 = 7 sin (θ) + 4

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

Solution steps

9 sin^{2} (θ) + 19 sin (θ) + 8 = 7 sin (θ) + 4

Solve by substitution

sin (θ) = - \frac{2}{3}

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

Combine all the solutions

θ = arcsin (- \frac{2}{3}) + 2 πn, θ = π + arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

arccos (x) = \frac{7 π}{8}

\frac{sin ( 3 7 ^{\circ} )}{23} = \frac{sin ( x )}{21}

csc (x) = \frac{1}{3}

(cot (x) + 1) (3 tan (x) - 1) = 0

2 cos^{2} (x) + sin (x) - 1 = 0, 0 \leq x \leq 2 π

What is the general solution for 9sin^2(θ)+19sin(θ)+8=7sin(θ)+4 ?
The general solution for 9sin^2(θ)+19sin(θ)+8=7sin(θ)+4 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin