What is the general solution for 4sin(x)=2sqrt(3) ?

The general solution for 4sin(x)=2sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin

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4sin(x)=2sqrt(3)

4 sin (x) = 23

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

4 sin (x) = 23

Divide both sides by

4

4 sin (x) = 23

Divide both sides by

4

\frac{4 sin ( x )}{4} = \frac{2 3}{4}

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 (x) = 180

2 sin^{2} (x) - 3 cos (- x) - 3 = 0

49.55 cos (θ) - 30 sin (θ) = 1.225

tan (2 x) + sin (2 x) + cos (2 x) = sec (2 x)

tan (x) cos^{2} (x) - tan (x) = 0, (0, 2 π)

What is the general solution for 4sin(x)=2sqrt(3) ?
The general solution for 4sin(x)=2sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin