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

The general solution for sin(4x)= 1/(sqrt(2)) is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2

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

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

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

Solution steps

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

Simplify

\frac{1}{2} : \frac{2}{2}

General solutions for

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

4 x = \frac{π}{4} + 2 πn, 4 x = \frac{3 π}{4} + 2 πn

Solve

4 x = \frac{π}{4} + 2 πn : x = \frac{π}{16} + \frac{πn}{2}

Solve

4 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

cot^{2} (x) + csc (x) = 1, 0 \leq x < 2 π

81 π = 10.5 - 9 cos (\frac{π}{30} t)

5 - 9 cos (x) = 0

tan^{2} (x) = 500

cot (x) + tan (x) = 1

What is the general solution for sin(4x)= 1/(sqrt(2)) ?
The general solution for sin(4x)= 1/(sqrt(2)) is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2