What is the general solution for sin(1/3 x)=0,0<= x<= 10pi ?

The general solution for sin(1/3 x)=0,0<= x<= 10pi is x=0,x=3pi,x=6pi,x=9pi

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sin(1/3 x)=0,0<= x<= 10pi

sin (\frac{1}{3} x) = 0, 0 \leq x \leq 10 π

x = 0, x = 3 π, x = 6 π, x = 9 π

Degrees

x = 0^{\circ}, x = 54 0^{\circ}, x = 108 0^{\circ}, x = 162 0^{\circ}

Solution steps

sin (\frac{1}{3} x) = 0, 0 \leq x \leq 10 π

General solutions for

sin (\frac{1}{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}

\frac{1}{3} x = 0 + 2 πn, \frac{1}{3} x = π + 2 πn

\frac{1}{3} x = 0 + 2 πn, \frac{1}{3} x = π + 2 πn

Solve

\frac{1}{3} x = 0 + 2 πn : x = 6 πn

\frac{1}{3} x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{1}{3} x = 2 πn

Multiply both sides by

3

\frac{1}{3} x = 2 πn

Multiply both sides by

3

3 \cdot \frac{1}{3} x = 3 \cdot 2 πn

Simplify

x = 6 πn

x = 6 πn

Solve

\frac{1}{3} x = π + 2 πn : x = 3 π + 6 πn

\frac{1}{3} x = π + 2 πn

Multiply both sides by

3

\frac{1}{3} x = π + 2 πn

Multiply both sides by

3

3 \cdot \frac{1}{3} x = 3 π + 3 \cdot 2 πn

Simplify

x = 3 π + 6 πn

x = 3 π + 6 πn

x = 6 πn, x = 3 π + 6 πn

Solutions for the range

0 \leq x \leq 10 π

x = 0, x = 3 π, x = 6 π, x = 9 π

sin (π y) = cos (1) sin (\frac{π}{6}) - \frac{1}{2}

0 = 4 cos (120 x)

(2 sin (x) - 1) (cos (x) - 2) = 0

7 - 6 sin (x) = 3 + 2 sin (x)

cos (θ) = \frac{2 \cdot 1 0 ^{- 5}}{54 \cdot 1 0 ^{- 6}}

What is the general solution for sin(1/3 x)=0,0<= x<= 10pi ?
The general solution for sin(1/3 x)=0,0<= x<= 10pi is x=0,x=3pi,x=6pi,x=9pi