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

The general solution for sin(x)= 1/4 ,sin(2x) is No Solution for x\in\mathbb{R}

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sin(x)= 1/4 ,sin(2x)

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

No Solution for x \in R

Solution steps

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

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

Solutions for the range

sin (2 x)

No Solution for x \in R

sin (θ) = 0.422

4 cos^{2} (x) + 3 cos (x) - 1 = 0

cos (x) = sin (x), 0 \leq x \leq 2 π

sin (4 (x - \frac{π}{4})) = 0

3 arcsin (2 θ) = 2 π

What is the general solution for sin(x)= 1/4 ,sin(2x) ?
The general solution for sin(x)= 1/4 ,sin(2x) is No Solution for x\in\mathbb{R}