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

The general solution for sin(0.5x)=0 is x=4pin,x=2pi+4pin

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Popular >

sin(0.5x)=0

Solution

sin (0.5 x) = 0

Solution

x = 4 πn, x = 2 π + 4 πn

Degrees

x = 0^{\circ} + 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

Solution steps

sin (0.5 x) = 0

General solutions for

sin (0.5 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}

0.5 x = 0 + 2 πn, 0.5 x = π + 2 πn

0.5 x = 0 + 2 πn, 0.5 x = π + 2 πn

Solve

0.5 x = 0 + 2 πn : x = 4 πn

0.5 x = 0 + 2 πn

0 + 2 πn = 2 πn

0.5 x = 2 πn

Multiply both sides by

10

0.5 x = 2 πn

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 x \cdot 10 = 2 πn \cdot 10

Refine

5 x = 20 πn

5 x = 20 πn

Divide both sides by

5

5 x = 20 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{20 πn}{5}

Simplify

x = 4 πn

x = 4 πn

Solve

0.5 x = π + 2 πn : x = 2 π + 4 πn

0.5 x = π + 2 πn

Multiply both sides by

10

0.5 x = π + 2 πn

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 x \cdot 10 = π 10 + 2 πn \cdot 10

Refine

5 x = 10 π + 20 πn

5 x = 10 π + 20 πn

Divide both sides by

5

5 x = 10 π + 20 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{10 π}{5} + \frac{20 πn}{5}

Simplify

\frac{5 x}{5} = \frac{10 π}{5} + \frac{20 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{10 π}{5} + \frac{20 πn}{5} : 2 π + 4 πn

\frac{10 π}{5} + \frac{20 πn}{5}

Divide the numbers:

\frac{10}{5} = 2

= 2 π + \frac{20 πn}{5}

Divide the numbers:

\frac{20}{5} = 4

= 2 π + 4 πn

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 4 πn, x = 2 π + 4 πn

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cos (2 x) = 2 - 3 sin (x), \frac{π}{2} \leq x \leq \frac{3 π}{2}

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4tan(x)+1=0

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Frequently Asked Questions (FAQ)

What is the general solution for sin(0.5x)=0 ?
The general solution for sin(0.5x)=0 is x=4pin,x=2pi+4pin