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

The general solution for sqrt(3)+2sin(x)=0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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sqrt(3)+2sin(x)=0

3 + 2 sin (x) = 0

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Degrees

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

3 + 2 sin (x) = 0

Move

3

to the right side

3 + 2 sin (x) = 0

Subtract

3

from both sides

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

Simplify

2 sin (x) = - 3

2 sin (x) = - 3

Divide both sides by

2

2 sin (x) = - 3

Divide both sides by

2

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

Simplify

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (x) = \frac{6}{4}

cot (x) sin^{2} (x) = 4 cot (x)

x, sin (x) + cos (y) = sin (x) cos (y)

x, z = arctan (\frac{x}{y})

- \frac{1}{2} = cos (θ)

What is the general solution for sqrt(3)+2sin(x)=0 ?
The general solution for sqrt(3)+2sin(x)=0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin