What is the general solution for sin^2(x)+5sin(x)=3 ?

The general solution for sin^2(x)+5sin(x)=3 is x=0.57207…+2pin,x=pi-0.57207…+2pin

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sin^2(x)+5sin(x)=3

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

x = 0.57207 \dots + 2 πn, x = π - 0.57207 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{- 5 + 37}{2}, sin (x) = \frac{- 5 - 37}{2}

sin (x) = \frac{- 5 + 37}{2} : x = arcsin (\frac{- 5 + 37}{2}) + 2 πn, x = π - arcsin (\frac{- 5 + 37}{2}) + 2 πn

sin (x) = \frac{- 5 - 37}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 5 + 37}{2}) + 2 πn, x = π - arcsin (\frac{- 5 + 37}{2}) + 2 πn

Show solutions in decimal form

x = 0.57207 \dots + 2 πn, x = π - 0.57207 \dots + 2 πn

14 + 7 cos (2 x) = 21 cos (x)

- 8 sin^{2} (θ) - 8 sin (θ) + 12 = - 5 sin (θ) + 7

cos (x) = 1 - 2 cos^{2} (x)

sin (3 x) = 0, 0 \leq x < 2 π

2 cos^{2} (x) = 3 cos (x)

What is the general solution for sin^2(x)+5sin(x)=3 ?
The general solution for sin^2(x)+5sin(x)=3 is x=0.57207…+2pin,x=pi-0.57207…+2pin