What is the general solution for sin^2(x)+5sin(x)=0 ?

The general solution for sin^2(x)+5sin(x)=0 is x=2pin,x=pi+2pin

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sin^2(x)+5sin(x)=0

sin^{2} (x) + 5 sin (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

sin^{2} (x) + 5 sin (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - 5

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 5 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan (α) = - \frac{4}{3}, \frac{π}{2} < α < π, cos (β) = \frac{1}{2}, 0 < β < \frac{π}{2}

- 3 cot (\frac{3 x}{2}) csc (\frac{3 x}{2}) = 0

sec (θ) = \frac{17}{8}

3 sin^{2} (x) = 1

3 sin (θ) + 5 = - 2 sin (θ)

What is the general solution for sin^2(x)+5sin(x)=0 ?
The general solution for sin^2(x)+5sin(x)=0 is x=2pin,x=pi+2pin