What is the general solution for sin^2(x)+5sin(x)-3=0 ?

The general solution for sin^2(x)+5sin(x)-3=0 is x=0.57207…+2pin,x=pi-0.57207…+2pin

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sin^2(x)+5sin(x)-3=0

sin^{2} (x) + 5 sin (x) - 3 = 0

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

Solution steps

sin^{2} (x) + 5 sin (x) - 3 = 0

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

2 - 3 sin (θ + \frac{4 π}{3}) = 2

tan (θ) = \frac{2}{6}

4 + 3 cos (x) = 0

3 sin^{2} (θ) - sin (θ) - 4 = 0

tan^{2} (x) = sin (x) sec (x)

What is the general solution for sin^2(x)+5sin(x)-3=0 ?
The general solution for sin^2(x)+5sin(x)-3=0 is x=0.57207…+2pin,x=pi-0.57207…+2pin