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

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

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1/4 =sin(x)

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

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

Degrees

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Switch sides

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

Apply trig inverse properties

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

General solutions for

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

sin (x) cos (x) - \frac{3}{2} sin (x) = 0

43 = arcsin (\frac{1}{x})

tan (x) sin (x) = tan (x)

csc (2 x) - 1 = 1

sin (2 t) = \frac{1}{8}

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