What is the general solution for sin(θ)= 1/4 ,0<θ< pi/2 ?

The general solution for sin(θ)= 1/4 ,0<θ< pi/2 is θ=0.25268…

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sin(θ)= 1/4 ,0<θ< pi/2

sin (θ) = \frac{1}{4}, 0 < θ < \frac{π}{2}

θ = 0.25268 \dots

Degrees

θ = 14.47751 \dots^{\circ}

Solution steps

sin (θ) = \frac{1}{4}, 0 < θ < \frac{π}{2}

Apply trig inverse properties

sin (θ) = \frac{1}{4}

General solutions for

sin (θ) = \frac{1}{4}

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

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

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

Solutions for the range

0 < θ < \frac{π}{2}

θ = arcsin (\frac{1}{4})

Show solutions in decimal form

θ = 0.25268 \dots

sin (2 θ) = \frac{1.35 \cdot 10}{( 38 ) ^{2}}

- 2 = \frac{16}{π} cos (4 \cdot x)

- (\frac{1}{2})^{2} + cos (θ^{2}) = 1

0 = 2 cos (2 θ)

2 sec^{2} (x) + tan (x) = 8

What is the general solution for sin(θ)= 1/4 ,0<θ< pi/2 ?
The general solution for sin(θ)= 1/4 ,0<θ< pi/2 is θ=0.25268…