What is the general solution for 0=1-cos(2pix) ?

The general solution for 0=1-cos(2pix) is x=n

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Popular Trigonometry >

0=1-cos(2pix)

Solution

0 = 1 - cos (2 π x)

Solution

x = n

Degrees

x = 0^{\circ}

Solution steps

0 = 1 - cos (2 π x)

Switch sides

1 - cos (2 π x) = 0

Move

1

to the right side

1 - cos (2 π x) = 0

Subtract

1

from both sides

1 - cos (2 π x) - 1 = 0 - 1

Simplify

- cos (2 π x) = - 1

- cos (2 π x) = - 1

Divide both sides by

- 1

- cos (2 π x) = - 1

Divide both sides by

- 1

\frac{- cos ( 2 π x )}{- 1} = \frac{- 1}{- 1}

Simplify

cos (2 π x) = 1

cos (2 π x) = 1

General solutions for

cos (2 π x) = 1

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 π x = 0 + 2 πn

2 π x = 0 + 2 πn

Solve

2 π x = 0 + 2 πn : x = n

2 π x = 0 + 2 πn

0 + 2 πn = 2 πn

2 π x = 2 πn

Divide both sides by

2 π

2 π x = 2 πn

Divide both sides by

2 π

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

Simplify

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{πn}{π}

Cancel the common factor:

π

= n

x = n

x = n

x = n

x = n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 0=1-cos(2pix) ?
The general solution for 0=1-cos(2pix) is x=n