What is the general solution for 0=-0.5sin(x/5) ?

The general solution for 0=-0.5sin(x/5) is x=10pin,x=5pi+10pin

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Popular >

0=-0.5sin(x/5)

Solution

0 = - 0.5 sin (\frac{x}{5})

Solution

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

0 = - 0.5 sin (\frac{x}{5})

Switch sides

- 0.5 sin (\frac{x}{5}) = 0

Multiply both sides by

10

- 0.5 sin (\frac{x}{5}) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

- 0.5 sin (\frac{x}{5}) \cdot 10 = 0 \cdot 10

Refine

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

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

Divide both sides by

- 5

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

Divide both sides by

- 5

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

Simplify

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

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

General solutions for

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

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

Solve

\frac{x}{5} = 0 + 2 πn : x = 10 πn

\frac{x}{5} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{5} = 2 πn

Multiply both sides by

5

\frac{x}{5} = 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 \cdot 2 πn

Simplify

x = 10 πn

x = 10 πn

Solve

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

\frac{x}{5} = π + 2 πn

Multiply both sides by

5

\frac{x}{5} = π + 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 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

Popular Examples

(408.4)/(sin(130))=(200)/(sin(x))

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

cot(θ)=-7/6

cot (θ) = - \frac{7}{6}

2/pi arccos(m*1-1)=0

\frac{2}{π} arccos (m \cdot 1 - 1) = 0

sin(θ)cos(θ)-1/2 cos(θ)=0

sin (θ) cos (θ) - \frac{1}{2} cos (θ) = 0

cos^2(60)+cos^2(45)+cos^2(x)=1

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

Frequently Asked Questions (FAQ)

What is the general solution for 0=-0.5sin(x/5) ?
The general solution for 0=-0.5sin(x/5) is x=10pin,x=5pi+10pin