What is the general solution for sin((3θ)/2)=0 ?

The general solution for sin((3θ)/2)=0 is θ=(4pin)/3 ,θ=(2pi)/3+(4pin)/3

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sin((3θ)/2)=0

sin (\frac{3 θ}{2}) = 0

θ = \frac{4 πn}{3}, θ = \frac{2 π}{3} + \frac{4 πn}{3}

Degrees

θ = 0^{\circ} + 24 0^{\circ} n, θ = 12 0^{\circ} + 24 0^{\circ} n

Solution steps

sin (\frac{3 θ}{2}) = 0

General solutions for

sin (\frac{3 θ}{2}) = 0

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}

\frac{3 θ}{2} = 0 + 2 πn, \frac{3 θ}{2} = π + 2 πn

\frac{3 θ}{2} = 0 + 2 πn, \frac{3 θ}{2} = π + 2 πn

Solve

\frac{3 θ}{2} = 0 + 2 πn : θ = \frac{4 πn}{3}

\frac{3 θ}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{3 θ}{2} = 2 πn

Multiply both sides by

2

\frac{3 θ}{2} = 2 πn

Multiply both sides by

2

\frac{2 \cdot 3 θ}{2} = 2 \cdot 2 πn

Simplify

3 θ = 4 πn

3 θ = 4 πn

Divide both sides by

3

3 θ = 4 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{4 πn}{3}

Simplify

θ = \frac{4 πn}{3}

θ = \frac{4 πn}{3}

Solve

\frac{3 θ}{2} = π + 2 πn : θ = \frac{2 π}{3} + \frac{4 πn}{3}

\frac{3 θ}{2} = π + 2 πn

Multiply both sides by

2

\frac{3 θ}{2} = π + 2 πn

Multiply both sides by

2

\frac{2 \cdot 3 θ}{2} = 2 π + 2 \cdot 2 πn

Simplify

3 θ = 2 π + 4 πn

3 θ = 2 π + 4 πn

Divide both sides by

3

3 θ = 2 π + 4 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{2 π}{3} + \frac{4 πn}{3}

Simplify

θ = \frac{2 π}{3} + \frac{4 πn}{3}

θ = \frac{2 π}{3} + \frac{4 πn}{3}

θ = \frac{4 πn}{3}, θ = \frac{2 π}{3} + \frac{4 πn}{3}

4 sin (\frac{π}{2} x) = 3

1 + cos (θ) = 2 cos (θ)

2 sin (x) cos (x) = - cos (x)

tan (2 t) = 0

3 cos (4 x - 26) + 5 = 7

What is the general solution for sin((3θ)/2)=0 ?
The general solution for sin((3θ)/2)=0 is θ=(4pin)/3 ,θ=(2pi)/3+(4pin)/3