What is the general solution for 8sin^2(x)=sin(x) ?

The general solution for 8sin^2(x)=sin(x) is x=0.12532…+2pin,x=pi-0.12532…+2pin,x=2pin,x=pi+2pin

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8sin^2(x)=sin(x)

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

x = 0.12532 \dots + 2 πn, x = π - 0.12532 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{1}{8}, sin (x) = 0

sin (x) = \frac{1}{8} : x = arcsin (\frac{1}{8}) + 2 πn, x = π - arcsin (\frac{1}{8}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{8}) + 2 πn, x = π - arcsin (\frac{1}{8}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.12532 \dots + 2 πn, x = π - 0.12532 \dots + 2 πn, x = 2 πn, x = π + 2 πn

6 cos (x) + 6 sin (x) = 36

3 sin (x) + 1 = 0

(tan (x) + 1) (cos (x) - 1) = 0

cot (θ) = - \frac{1}{3}

32 cos (θ) + 3 = 6

What is the general solution for 8sin^2(x)=sin(x) ?
The general solution for 8sin^2(x)=sin(x) is x=0.12532…+2pin,x=pi-0.12532…+2pin,x=2pin,x=pi+2pin