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

The general solution for 2sin(3x)=sqrt(3) is x= pi/9+(2pin)/3 ,x=(2pi)/9+(2pin)/3

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2sin(3x)=sqrt(3)

2 sin (3 x) = 3

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{2 π}{9} + \frac{2 πn}{3}

Solution steps

2 sin (3 x) = 3

Divide both sides by

2

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

General solutions for

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

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

Solve

3 x = \frac{π}{3} + 2 πn : x = \frac{π}{9} + \frac{2 πn}{3}

Solve

3 x = \frac{2 π}{3} + 2 πn : x = \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{2 π}{9} + \frac{2 πn}{3}

4 sin (3 θ) = 7 cos (3 θ), 0^{\circ} \leq 3 θ < 72 0^{\circ}

cot (θ) = 4

2 sin (\frac{1}{2} x) + 3 = 0

0 = - \frac{1}{7} cos (7 t)

cos (α) = \frac{5}{13}

What is the general solution for 2sin(3x)=sqrt(3) ?
The general solution for 2sin(3x)=sqrt(3) is x= pi/9+(2pin)/3 ,x=(2pi)/9+(2pin)/3