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

The general solution for -4+4sin(x)=-2 is x= pi/6+2pin,x=(5pi)/6+2pin

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-4+4sin(x)=-2

- 4 + 4 sin (x) = - 2

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

- 4 + 4 sin (x) = - 2

Move

4

to the right side

- 4 + 4 sin (x) = - 2

Add

4

to both sides

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

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

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{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x + π) + sin (x - π) = 0

cos (y) - sin (y) = 0

36 sin (x) cos (x) = - 93

sin (2 x) = cos (4 x)

6 cos^{2} (θ) + 7 = - 17 cos (θ)

What is the general solution for -4+4sin(x)=-2 ?
The general solution for -4+4sin(x)=-2 is x= pi/6+2pin,x=(5pi)/6+2pin