What is the general solution for 2sin^2(x)+3sin(x)-1=0 ?

The general solution for 2sin^2(x)+3sin(x)-1=0 is x=0.28460…+2pin,x=pi-0.28460…+2pin

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2sin^2(x)+3sin(x)-1=0

2 sin^{2} (x) + 3 sin (x) - 1 = 0

x = 0.28460 \dots + 2 πn, x = π - 0.28460 \dots + 2 πn

Solution steps

2 sin^{2} (x) + 3 sin (x) - 1 = 0

Solve by substitution

sin (x) = \frac{- 3 + 17}{4}, sin (x) = \frac{- 3 - 17}{4}

sin (x) = \frac{- 3 + 17}{4} : x = arcsin (\frac{- 3 + 17}{4}) + 2 πn, x = π - arcsin (\frac{- 3 + 17}{4}) + 2 πn

sin (x) = \frac{- 3 - 17}{4} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 3 + 17}{4}) + 2 πn, x = π - arcsin (\frac{- 3 + 17}{4}) + 2 πn

Show solutions in decimal form

x = 0.28460 \dots + 2 πn, x = π - 0.28460 \dots + 2 πn

- 6 cos^{2} (θ) + cos (θ) + 7 = 5

y, arccot (x y) = ln (sin (x))

tan (α) = - \frac{3}{4}

sec (2 x) csc (2 x) = 2 csc (2 x), 0 \leq x \leq 2 π

tan^{2} (x) - 3 tan (x) - 10 = 0

What is the general solution for 2sin^2(x)+3sin(x)-1=0 ?
The general solution for 2sin^2(x)+3sin(x)-1=0 is x=0.28460…+2pin,x=pi-0.28460…+2pin