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

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

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sin(α)= 1/4

sin (α) = \frac{1}{4}

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

Degrees

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

Solution steps

sin (α) = \frac{1}{4}

Apply trig inverse properties

sin (α) = \frac{1}{4}

General solutions for

sin (α) = \frac{1}{4}

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

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

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

Show solutions in decimal form

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

3 cos^{2} (3 x) - \frac{9}{4} = 0

4 sin (θ) - 1 = 0

2 sin (x) 4 + 3 = 0

arctan (\frac{y}{- 1}) = 13 5^{\circ}

2 cos^{2} (x) + 3 cos (x) - 2 = 0, - π \leq x \leq π

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