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

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

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

- 2 sin (x) + 3 = 0

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

- 2 sin (x) + 3 = 0

Move

3

to the right side

- 2 sin (x) + 3 = 0

Subtract

3

from both sides

- 2 sin (x) + 3 - 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

sin (θ) = \frac{4}{5}, cos (θ) = \frac{3}{5}

sec (2 x) + tan (2 x) = 8

cos (θ) = \frac{1}{12}

sin (θ) = - \frac{8}{9}

2 sin^{2} (x) + 5 sin (x) - 12 = 0

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