What is the general solution for 5sin^2(x)+10sin(x)+2=0 ?

The general solution for 5sin^2(x)+10sin(x)+2=0 is x=-0.22735…+2pin,x=pi+0.22735…+2pin

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5sin^2(x)+10sin(x)+2=0

5 sin^{2} (x) + 10 sin (x) + 2 = 0

x = - 0.22735 \dots + 2 πn, x = π + 0.22735 \dots + 2 πn

Solution steps

5 sin^{2} (x) + 10 sin (x) + 2 = 0

Solve by substitution

sin (x) = \frac{- 5 + 15}{5}, sin (x) = - \frac{5 + 15}{5}

sin (x) = \frac{- 5 + 15}{5} : x = arcsin (\frac{- 5 + 15}{5}) + 2 πn, x = π + arcsin (- \frac{- 5 + 15}{5}) + 2 πn

sin (x) = - \frac{5 + 15}{5} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 5 + 15}{5}) + 2 πn, x = π + arcsin (- \frac{- 5 + 15}{5}) + 2 πn

Show solutions in decimal form

x = - 0.22735 \dots + 2 πn, x = π + 0.22735 \dots + 2 πn

tan (x) = \frac{5}{5.1}

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

8 sin (θ) + 15 cos (θ) = 0

sin (t) = \frac{3}{7}

cos (2 x - 1) = sin (3 x + 6)

What is the general solution for 5sin^2(x)+10sin(x)+2=0 ?
The general solution for 5sin^2(x)+10sin(x)+2=0 is x=-0.22735…+2pin,x=pi+0.22735…+2pin