What is the general solution for sin^3(x)= 1/8 ?

The general solution for sin^3(x)= 1/8 is x= pi/6+2pin,x=(5pi)/6+2pin

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sin^3(x)= 1/8

sin^{3} (x) = \frac{1}{8}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

sin^{3} (x) = \frac{1}{8}

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - \frac{1}{4} + i \frac{3}{4}, sin (x) = - \frac{1}{4} - i \frac{3}{4}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - \frac{1}{4} + i \frac{3}{4} :

No Solution

sin (x) = - \frac{1}{4} - i \frac{3}{4} :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

y, sin (y^{2}) = x

cos (7 x) = - \frac{3}{2}

y, x sin (y) + cos (x) = 1

cos (x) = - sin^{2} (x)

x, cos^{2} (x) = 2 - 2 sin (x)

What is the general solution for sin^3(x)= 1/8 ?
The general solution for sin^3(x)= 1/8 is x= pi/6+2pin,x=(5pi)/6+2pin