What is the general solution for sin^2(x)+6sin(x)+5=0 ?

The general solution for sin^2(x)+6sin(x)+5=0 is x=(3pi)/2+2pin

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sin^2(x)+6sin(x)+5=0

sin^{2} (x) + 6 sin (x) + 5 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) + 6 sin (x) + 5 = 0

Solve by substitution

sin (x) = - 1, sin (x) = - 5

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

sin (x) = - 5 :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

cos (x) = \frac{1}{3}, 0 < x < \frac{π}{2}

3 + 2 sin (θ) = 3 + 2 cos (θ)

\frac{sin ( x )}{cos ( x )} = \frac{1}{3}

5 sin (θ) + 4 = 0

sin (\frac{5 x}{2}) = 0

What is the general solution for sin^2(x)+6sin(x)+5=0 ?
The general solution for sin^2(x)+6sin(x)+5=0 is x=(3pi)/2+2pin