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

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

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

0 = 3 - 2 sin (x)

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = 3 - 2 sin (x)

Switch sides

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

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

- 2 sin^{2} (θ) + cos (θ) = - 1

4 cos (θ) = 4 (1 - cos (θ))

2 cos (x) = 1.7

sin (2 x + 30) = 0.8

1 - 2 sin (x) = - 1

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