What is the general solution for sin(1/5 x)=0 ?

The general solution for sin(1/5 x)=0 is x=10pin,x=5pi+10pin

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sin(1/5 x)=0

sin (\frac{1}{5} x) = 0

x = 10 πn, x = 5 π + 10 πn

Degrees

x = 0^{\circ} + 180 0^{\circ} n, x = 90 0^{\circ} + 180 0^{\circ} n

Solution steps

sin (\frac{1}{5} x) = 0

General solutions for

sin (\frac{1}{5} 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}{5} x = 0 + 2 πn, \frac{1}{5} x = π + 2 πn

\frac{1}{5} x = 0 + 2 πn, \frac{1}{5} x = π + 2 πn

Solve

\frac{1}{5} x = 0 + 2 πn : x = 10 πn

\frac{1}{5} x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{1}{5} x = 2 πn

Multiply both sides by

5

\frac{1}{5} x = 2 πn

Multiply both sides by

5

5 \cdot \frac{1}{5} x = 5 \cdot 2 πn

Simplify

x = 10 πn

x = 10 πn

Solve

\frac{1}{5} x = π + 2 πn : x = 5 π + 10 πn

\frac{1}{5} x = π + 2 πn

Multiply both sides by

5

\frac{1}{5} x = π + 2 πn

Multiply both sides by

5

5 \cdot \frac{1}{5} x = 5 π + 5 \cdot 2 πn

Simplify

x = 5 π + 10 πn

x = 5 π + 10 πn

x = 10 πn, x = 5 π + 10 πn

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

sin (2 x) + sin (x) - sin (3 x) = 0

tan (x) = \frac{3}{10}

arccos (2 x) + arccos (x) = \frac{π}{3}

1.74 \cdot sin (40.3 1^{\circ}) = 1.33 \cdot sin (θ)

What is the general solution for sin(1/5 x)=0 ?
The general solution for sin(1/5 x)=0 is x=10pin,x=5pi+10pin