What is the general solution for 3sin^2(x)+4sin(x)+1=0 ?

The general solution for 3sin^2(x)+4sin(x)+1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin,x=(3pi)/2+2pin

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3sin^2(x)+4sin(x)+1=0

3 sin^{2} (x) + 4 sin (x) + 1 = 0

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

3 sin^{2} (x) + 4 sin (x) + 1 = 0

Solve by substitution

sin (x) = - \frac{1}{3}, sin (x) = - 1

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

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

Combine all the solutions

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn, x = \frac{3 π}{2} + 2 πn

Show solutions in decimal form

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = \frac{9}{14}

sin (θ) = \frac{7}{9}

cos (θ) = 0.97617

cos (a) = 0, 99 9^{99} x, \frac{sin ( a )}{cos ( a )} x

sin (\frac{x}{2} + π) = \frac{3}{2 3}

What is the general solution for 3sin^2(x)+4sin(x)+1=0 ?
The general solution for 3sin^2(x)+4sin(x)+1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin,x=(3pi)/2+2pin