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

The general solution for 5sin^2(x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=-0.41151…+2pin,x=pi+0.41151…+2pin

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

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

x = 2 πn, x = π + 2 πn, x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

Solution steps

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

x, y^{3} + 7 y^{2} + y + 7 = 2 cos (x)

cos (2 x) - 11 cos (x) + 6 = 0

x, sin (x) = \frac{1}{2}

- 2 cos (x) + 1 = 5 cos (x) + 0

sin (x) = - 0.45

What is the general solution for 5sin^2(x)+2sin(x)=0 ?
The general solution for 5sin^2(x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=-0.41151…+2pin,x=pi+0.41151…+2pin