What is the general solution for sin(x/4)=0 ?

The general solution for sin(x/4)=0 is x=8pin,x=4pi+8pin

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sin(x/4)=0

sin (\frac{x}{4}) = 0

x = 8 πn, x = 4 π + 8 πn

Degrees

x = 0^{\circ} + 144 0^{\circ} n, x = 72 0^{\circ} + 144 0^{\circ} n

Solution steps

sin (\frac{x}{4}) = 0

General solutions for

sin (\frac{x}{4}) = 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{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

Solve

\frac{x}{4} = 0 + 2 πn : x = 8 πn

\frac{x}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{4} = 2 πn

Multiply both sides by

4

\frac{x}{4} = 2 πn

Multiply both sides by

4

\frac{4 x}{4} = 4 \cdot 2 πn

Simplify

x = 8 πn

x = 8 πn

Solve

\frac{x}{4} = π + 2 πn : x = 4 π + 8 πn

\frac{x}{4} = π + 2 πn

Multiply both sides by

4

\frac{x}{4} = π + 2 πn

Multiply both sides by

4

\frac{4 x}{4} = 4 π + 4 \cdot 2 πn

Simplify

x = 4 π + 8 πn

x = 4 π + 8 πn

x = 8 πn, x = 4 π + 8 πn

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^{2} (x) + sec (x) - 2 = 0

(cot (x) - 1) (2 sin (x) + 1) = 0

What is the general solution for sin(x/4)=0 ?
The general solution for sin(x/4)=0 is x=8pin,x=4pi+8pin