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

The general solution for 6sin^2(x)+5sin(x)=0 is x=2pin,x=pi+2pin,x=-0.98511…+2pin,x=pi+0.98511…+2pin

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

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

x = 2 πn, x = π + 2 πn, x = - 0.98511 \dots + 2 πn, x = π + 0.98511 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = 0, sin (x) = - \frac{5}{6}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arcsin (- \frac{5}{6}) + 2 πn, x = π + arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 0.98511 \dots + 2 πn, x = π + 0.98511 \dots + 2 πn

sin (x) = - \frac{1}{2}, (0, 2 π)

tan (θ) = \frac{4}{3}, cos (θ) < 0

cot (x) = \frac{sin ( x )}{cos ( x )}

0.6 = \frac{cosh ( 0.2 m )}{cosh ( 0.4 m )}

12 cos (2 x) + 5 sin (x) - 9 = 0

What is the general solution for 6sin^2(x)+5sin(x)=0 ?
The general solution for 6sin^2(x)+5sin(x)=0 is x=2pin,x=pi+2pin,x=-0.98511…+2pin,x=pi+0.98511…+2pin