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

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

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sin^3(t)= 1/8

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

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

Solution steps

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

Solve by substitution

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

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

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

No Solution

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

No Solution

Combine all the solutions

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

2 cos (t) \cdot sin (t) = cos (t)

sin (x) (5 sin (x) + 5) = 0

csc (θ) = \frac{- 3}{5}

sec^{2} (x) + tan^{2} (x) = 5 tan (x)

sin (x) = \frac{9}{12}

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