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=0.30760…+2pin,x=pi-0.30760…+2pin

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

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

x = 0.30760 \dots + 2 πn, x = π - 0.30760 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{- 3 + 13}{2}, sin (x) = \frac{- 3 - 13}{2}

sin (x) = \frac{- 3 + 13}{2} : x = arcsin (\frac{- 3 + 13}{2}) + 2 πn, x = π - arcsin (\frac{- 3 + 13}{2}) + 2 πn

sin (x) = \frac{- 3 - 13}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 3 + 13}{2}) + 2 πn, x = π - arcsin (\frac{- 3 + 13}{2}) + 2 πn

Show solutions in decimal form

x = 0.30760 \dots + 2 πn, x = π - 0.30760 \dots + 2 πn

tan (x) - 3^{\frac{1}{2}} = 0

\frac{1 + ( 2 sin ( x ) )}{( cos ( x ) )} = 0

\frac{sin ^{2} ( a )}{2} = \frac{1 - cos ( a )}{2}

\frac{cot ^{2} ( x )}{2} = 3

sin (x - 3 0^{\circ}) = 0.7

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=0.30760…+2pin,x=pi-0.30760…+2pin