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

The general solution for sin^2(x)+3sin(x)+1=0 is x=-0.39192…+2pin,x=pi+0.39192…+2pin

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

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

x = - 0.39192 \dots + 2 πn, x = π + 0.39192 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{- 3 + 5}{2}, sin (x) = \frac{- 3 - 5}{2}

sin (x) = \frac{- 3 + 5}{2} : x = arcsin (\frac{- 3 + 5}{2}) + 2 πn, x = π + arcsin (- \frac{- 3 + 5}{2}) + 2 πn

sin (x) = \frac{- 3 - 5}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 3 + 5}{2}) + 2 πn, x = π + arcsin (- \frac{- 3 + 5}{2}) + 2 πn

Show solutions in decimal form

x = - 0.39192 \dots + 2 πn, x = π + 0.39192 \dots + 2 πn

8 sin (b) + 1 = sin (b) + 1

7 cos (3 x) = 7

cos^{2} (θ) = sin^{2} (θ) + 1

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) - 1 = 0

\frac{1}{2} sin (x) = - \frac{3}{4}

What is the general solution for sin^2(x)+3sin(x)+1=0 ?
The general solution for sin^2(x)+3sin(x)+1=0 is x=-0.39192…+2pin,x=pi+0.39192…+2pin