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

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

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

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

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

Solution steps

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

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

tan (θ) = 0.3249

sec^{2} (θ) + tan (θ) = 1

cos (\frac{1}{2} x) + 1 = 0

cos (x) + 5 = 5

cos^{2} (x) + cos (x) + 1 = 0

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