What is the general solution for sin(x)=\pm 1/(sqrt(2)) ?

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

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sin(x)=\pm 1/(sqrt(2))

sin (x) = \pm \frac{1}{2}

No Solution for x \in R

Solution steps

sin (x) = \pm \frac{1}{2}

Apply trig inverse properties

sin (x) = \pm \frac{1}{2}

General solutions for

sin (x) = \pm \frac{1}{2}

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

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

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

Since the equation is undefined for:

arcsin (\pm \frac{1}{2}) + 2 πn, π + arcsin (- \pm \frac{1}{2}) + 2 πn

No Solution for x \in R

30 = 211.49 - 20.96 cosh (0.03291765 x)

tan (θ) = \frac{2}{- 3}

x, z = arcsin (\frac{x y}{x ^{2} + y ^{2}})

\frac{tan ( x ) + cos ( x )}{( 1 + sin ( x ) )} = \frac{1}{cos ( x )}

sin (θ) = \frac{4}{5}, 0 \leq θ \leq \frac{π}{2}

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