What is the general solution for -8sin(8x)=0 ?

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

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-8sin(8x)=0

- 8 sin (8 x) = 0

x = \frac{πn}{4}, x = \frac{π}{8} + \frac{πn}{4}

Degrees

x = 0^{\circ} + 4 5^{\circ} n, x = 22. 5^{\circ} + 4 5^{\circ} n

Solution steps

- 8 sin (8 x) = 0

Divide both sides by

- 8

- 8 sin (8 x) = 0

Divide both sides by

- 8

\frac{- 8 sin ( 8 x )}{- 8} = \frac{0}{- 8}

Simplify

sin (8 x) = 0

sin (8 x) = 0

General solutions for

sin (8 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}

8 x = 0 + 2 πn, 8 x = π + 2 πn

8 x = 0 + 2 πn, 8 x = π + 2 πn

Solve

8 x = 0 + 2 πn : x = \frac{πn}{4}

8 x = 0 + 2 πn

0 + 2 πn = 2 πn

8 x = 2 πn

Divide both sides by

8

8 x = 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{2 πn}{8}

Simplify

x = \frac{πn}{4}

x = \frac{πn}{4}

Solve

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

8 x = π + 2 πn

Divide both sides by

8

8 x = π + 2 πn

Divide both sides by

8

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

Simplify

x = \frac{π}{8} + \frac{πn}{4}

x = \frac{π}{8} + \frac{πn}{4}

x = \frac{πn}{4}, x = \frac{π}{8} + \frac{πn}{4}

sin (θ) = - \frac{7}{25}

cos (\frac{θ}{2}) = - \frac{3}{2}

2 sin^{2} (x) = - sin (x)

3 sec (θ) = 2

cosh (x) = - 1

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