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

The general solution for 3sin^2(θ)=2sin(θ)+3 is θ=-0.80489…+2pin,θ=pi+0.80489…+2pin

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3sin^2(θ)=2sin(θ)+3

3 sin^{2} (θ) = 2 sin (θ) + 3

θ = - 0.80489 \dots + 2 πn, θ = π + 0.80489 \dots + 2 πn

Solution steps

3 sin^{2} (θ) = 2 sin (θ) + 3

Solve by substitution

sin (θ) = \frac{1 + 10}{3}, sin (θ) = \frac{1 - 10}{3}

sin (θ) = \frac{1 + 10}{3} :

No Solution

sin (θ) = \frac{1 - 10}{3} : θ = arcsin (\frac{1 - 10}{3}) + 2 πn, θ = π + arcsin (- \frac{1 - 10}{3}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{1 - 10}{3}) + 2 πn, θ = π + arcsin (- \frac{1 - 10}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.80489 \dots + 2 πn, θ = π + 0.80489 \dots + 2 πn

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

(sin (x) + cos (x))^{2} = 1^{2}

tan (4 x) = 12

4 csc (B) + 5 = 0

2 cos (\frac{π}{5} x) = 3

What is the general solution for 3sin^2(θ)=2sin(θ)+3 ?
The general solution for 3sin^2(θ)=2sin(θ)+3 is θ=-0.80489…+2pin,θ=pi+0.80489…+2pin