What is the general solution for 3-sin(x)(4+6sin(x))=0 ?

The general solution for 3-sin(x)(4+6sin(x))=0 is x=0.46497…+2pin,x=pi-0.46497…+2pin

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3-sin(x)(4+6sin(x))=0

3 - sin (x) (4 + 6 sin (x)) = 0

x = 0.46497 \dots + 2 πn, x = π - 0.46497 \dots + 2 πn

Solution steps

3 - sin (x) (4 + 6 sin (x)) = 0

Solve by substitution

sin (x) = - \frac{2 + 22}{6}, sin (x) = \frac{22 - 2}{6}

sin (x) = - \frac{2 + 22}{6} :

No Solution

sin (x) = \frac{22 - 2}{6} : x = arcsin (\frac{22 - 2}{6}) + 2 πn, x = π - arcsin (\frac{22 - 2}{6}) + 2 πn

Combine all the solutions

x = arcsin (\frac{22 - 2}{6}) + 2 πn, x = π - arcsin (\frac{22 - 2}{6}) + 2 πn

Show solutions in decimal form

x = 0.46497 \dots + 2 πn, x = π - 0.46497 \dots + 2 πn

cos (a) = - \frac{3}{5}, sin (a) > 0

cot (x) - cot (33.4 7^{\circ}) = \frac{1485}{2460}

3 + \frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) = 3

sin (θ) = - \frac{13}{7}

- 2 sin (x) = - 2

What is the general solution for 3-sin(x)(4+6sin(x))=0 ?
The general solution for 3-sin(x)(4+6sin(x))=0 is x=0.46497…+2pin,x=pi-0.46497…+2pin