What is the general solution for 0=-0.65sin(13x) ?

The general solution for 0=-0.65sin(13x) is x=(2pin)/(13),x= pi/(13)+(2pin)/(13)

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0=-0.65sin(13x)

0 = - 0.65 sin (13 x)

x = \frac{2 πn}{13}, x = \frac{π}{13} + \frac{2 πn}{13}

Degrees

x = 0^{\circ} + 27.69230 \dots^{\circ} n, x = 13.84615 \dots^{\circ} + 27.69230 \dots^{\circ} n

Solution steps

0 = - 0.65 sin (13 x)

Switch sides

- 0.65 sin (13 x) = 0

Multiply both sides by

100

- 0.65 sin (13 x) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 0.65 sin (13 x) \cdot 100 = 0 \cdot 100

Refine

- 65 sin (13 x) = 0

- 65 sin (13 x) = 0

Divide both sides by

- 65

- 65 sin (13 x) = 0

Divide both sides by

- 65

\frac{- 65 sin ( 13 x )}{- 65} = \frac{0}{- 65}

Simplify

sin (13 x) = 0

sin (13 x) = 0

General solutions for

sin (13 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}

13 x = 0 + 2 πn, 13 x = π + 2 πn

13 x = 0 + 2 πn, 13 x = π + 2 πn

Solve

13 x = 0 + 2 πn : x = \frac{2 πn}{13}

13 x = 0 + 2 πn

0 + 2 πn = 2 πn

13 x = 2 πn

Divide both sides by

13

13 x = 2 πn

Divide both sides by

13

\frac{13 x}{13} = \frac{2 πn}{13}

Simplify

x = \frac{2 πn}{13}

x = \frac{2 πn}{13}

Solve

13 x = π + 2 πn : x = \frac{π}{13} + \frac{2 πn}{13}

13 x = π + 2 πn

Divide both sides by

13

13 x = π + 2 πn

Divide both sides by

13

\frac{13 x}{13} = \frac{π}{13} + \frac{2 πn}{13}

Simplify

x = \frac{π}{13} + \frac{2 πn}{13}

x = \frac{π}{13} + \frac{2 πn}{13}

x = \frac{2 πn}{13}, x = \frac{π}{13} + \frac{2 πn}{13}

What is the general solution for 0=-0.65sin(13x) ?
The general solution for 0=-0.65sin(13x) is x=(2pin)/(13),x= pi/(13)+(2pin)/(13)