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

The general solution for 4sin(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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4sin(x)+2=0

4 sin (x) + 2 = 0

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Degrees

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (x) + 2 = 0

Move

2

to the right side

4 sin (x) + 2 = 0

Subtract

2

from both sides

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

Simplify

4 sin (x) = - 2

4 sin (x) = - 2

Divide both sides by

4

4 sin (x) = - 2

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 sin ( x )}{4} : sin (x)

\frac{4 sin ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (x)

Simplify

\frac{- 2}{4} : - \frac{1}{2}

\frac{- 2}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{4}

Cancel the common factor:

2

= - \frac{1}{2}

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

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

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

General solutions for

sin (x) = - \frac{1}{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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

cot (θ) = 2

tan (t) = \frac{2}{3}

2 sin (x) tan (x) = - tan (x)

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

sec (θ) = tan (θ) + cot (θ)

What is the general solution for 4sin(x)+2=0 ?
The general solution for 4sin(x)+2=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin