What is the general solution for sin(2x)= 1/4 ?

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

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sin(2x)= 1/4

sin (2 x) = \frac{1}{4}

x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

Solution steps

sin (2 x) = \frac{1}{4}

Apply trig inverse properties

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

Solve

2 x = arcsin (\frac{1}{4}) + 2 πn : x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

Solve

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

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

Show solutions in decimal form

x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

sin^{2} (x) = \frac{1}{8}

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

cosh (4 x) = 16 sinh (x) + 1

cos (θ) = (\frac{3}{2})

cos (x + \frac{3 π}{4}) + cos (x - \frac{3 π}{4}) = 1

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