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

The general solution for sqrt(3)=2sqrt(3)sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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

3 = 23 sin (x)

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

3 = 23 sin (x)

Switch sides

23 sin (x) = 3

Divide both sides by

23

23 sin (x) = 3

Divide both sides by

23

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

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

8 cos (6 x) = 2

sin (x) = \frac{- ( 6 )}{( 7 ) cos ( x )}

5^{2} = 8^{2} - (11.85)^{2} - 2 (8) (11.85) (cos (A))

2 + 2 sin (θ) = 4

- 4 sin (8 x) = 0

What is the general solution for sqrt(3)=2sqrt(3)sin(x) ?
The general solution for sqrt(3)=2sqrt(3)sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin