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} :

No Solution

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

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

2 sin (6 x) - 1 = 0

sin^{2} (x) = \frac{( 6 m - 5 )}{5}

sin^{2} (θ) - sin (θ) - 6 = 0

cos (2 θ) - 3 cos (θ) + 2 = 0

u, x = 2 tanh (u)

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