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

The general solution for sin^2(x)+3sin(x)-2=0 is x=0.59626…+2pin,x=pi-0.59626…+2pin

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

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

x = 0.59626 \dots + 2 πn, x = π - 0.59626 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{- 3 + 17}{2}, sin (x) = \frac{- 3 - 17}{2}

sin (x) = \frac{- 3 + 17}{2} : x = arcsin (\frac{- 3 + 17}{2}) + 2 πn, x = π - arcsin (\frac{- 3 + 17}{2}) + 2 πn

sin (x) = \frac{- 3 - 17}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 3 + 17}{2}) + 2 πn, x = π - arcsin (\frac{- 3 + 17}{2}) + 2 πn

Show solutions in decimal form

x = 0.59626 \dots + 2 πn, x = π - 0.59626 \dots + 2 πn

cos (θ) = 0.9848

tan (x) = \frac{7}{4}

cos (θ) = \frac{2 5}{5}

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

- 3 sin (x) + 2 = 0

What is the general solution for sin^2(x)+3sin(x)-2=0 ?
The general solution for sin^2(x)+3sin(x)-2=0 is x=0.59626…+2pin,x=pi-0.59626…+2pin