What is the general solution for sin(x)-1/4 =0 ?

The general solution for sin(x)-1/4 =0 is x=0.25268…+2pin,x=pi-0.25268…+2pin

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sin(x)-1/4 =0

sin (x) - \frac{1}{4} = 0

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

sin (x) - \frac{1}{4} = 0

Move

\frac{1}{4}

to the right side

sin (x) - \frac{1}{4} = 0

Add

\frac{1}{4}

to both sides

sin (x) - \frac{1}{4} + \frac{1}{4} = 0 + \frac{1}{4}

Simplify

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

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

2 csc (θ) - 2 = 0

sin (θ) = \frac{5}{4}

100 = 5040 cos (θ)

cos (3 x) = \frac{2}{3}

cos (x) (csc (x) + 2) = 0

What is the general solution for sin(x)-1/4 =0 ?
The general solution for sin(x)-1/4 =0 is x=0.25268…+2pin,x=pi-0.25268…+2pin