What is the general solution for sin(x)= 1/4 ?

The general solution for sin(x)= 1/4 is x=0.25268…+2pin,x=pi-0.25268…+2pin

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sin(x)= 1/4

sin (x) = \frac{1}{4}

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Solution steps

sin (x) = \frac{1}{4}

Apply trig inverse properties

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

2 sin^{2} (x) - 5 sin (x) + 2 = 0

sin (x + \frac{π}{3}) + sin (x - \frac{π}{3}) = 1

sec^{2} (x) = 4

1 + 2 cos (x) = 0

sin (2 x) = 3 cos (x)

What is the general solution for sin(x)= 1/4 ?
The general solution for sin(x)= 1/4 is x=0.25268…+2pin,x=pi-0.25268…+2pin