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

The general solution for sin^3(x)=-1 is x=(3pi)/2+2pin

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sin^3(x)=-1

sin^{3} (x) = - 1

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{3} (x) = - 1

Solve by substitution

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

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = \frac{1}{2} - i \frac{3}{2} :

No Solution

sin (x) = \frac{1}{2} + i \frac{3}{2} :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

x, sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

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

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

sin^{3} (x) - 2 sin (x) = 0

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