What is the general solution for -8sin^2(x)+22sin(x)=12 ?

The general solution for -8sin^2(x)+22sin(x)=12 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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-8sin^2(x)+22sin(x)=12

- 8 sin^{2} (x) + 22 sin (x) = 12

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

- 8 sin^{2} (x) + 22 sin (x) = 12

Solve by substitution

sin (x) = \frac{3}{4}, sin (x) = 2

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

sin (x) = 2 :

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

cos (θ) = \frac{1}{5}

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

cot^{2} (x) = cot^{2} (x) - 2 cot (x)

cos (x) = \frac{4}{10}

16 cos (2 x) - 4 = 0

What is the general solution for -8sin^2(x)+22sin(x)=12 ?
The general solution for -8sin^2(x)+22sin(x)=12 is x=0.84806…+2pin,x=pi-0.84806…+2pin