What is the general solution for 3|sin(3x)|=0 ?

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

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3|sin(3x)|=0

3 ∣ sin (3 x) ∣ = 0

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

Degrees

x = 0^{\circ} + 12 0^{\circ} n, x = 6 0^{\circ} + 12 0^{\circ} n

Solution steps

3 ∣ sin (3 x) ∣ = 0

Divide both sides by

3

3 ∣ sin (3 x) ∣ = 0

Divide both sides by

3

\frac{3 ∣ sin ( 3 x ) ∣}{3} = \frac{0}{3}

Simplify

∣ sin (3 x) ∣ = 0

∣ sin (3 x) ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

sin (3 x) = 0

General solutions for

sin (3 x) = 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}

3 x = 0 + 2 πn, 3 x = π + 2 πn

3 x = 0 + 2 πn, 3 x = π + 2 πn

Solve

3 x = 0 + 2 πn : x = \frac{2 πn}{3}

3 x = 0 + 2 πn

0 + 2 πn = 2 πn

3 x = 2 πn

Divide both sides by

3

3 x = 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 πn}{3}

Simplify

x = \frac{2 πn}{3}

x = \frac{2 πn}{3}

Solve

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

3 x = π + 2 πn

Divide both sides by

3

3 x = π + 2 πn

Divide both sides by

3

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

Simplify

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

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

\frac{75}{125} = \frac{cosh ( 0.2 x )}{cosh ( 0.4 x )}

sec (4 x) - (\frac{2}{3}) = 0

3 cos (x) + 6 = cos (x) + 5

cos (x) = \frac{1}{3}, \frac{3 π}{2} < x < 2 π

\frac{2.68}{sin ( 12 6 ^{\circ} )} = \frac{1.2}{sin ( x )}

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