What is the general solution for 2cos(x/3)-sqrt(2)=0 ?

The general solution for 2cos(x/3)-sqrt(2)=0 is x=(3pi)/4+6pin,x=(21pi)/4+6pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(x/3)-sqrt(2)=0

Solution

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

Solution

x = \frac{3 π}{4} + 6 πn, x = \frac{21 π}{4} + 6 πn

Degrees

x = 13 5^{\circ} + 108 0^{\circ} n, x = 94 5^{\circ} + 108 0^{\circ} n

Solution steps

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

Move

2

to the right side

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

Add

2

to both sides

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

Simplify

2 cos (\frac{x}{3}) = 2

2 cos (\frac{x}{3}) = 2

Divide both sides by

2

2 cos (\frac{x}{3}) = 2

Divide both sides by

2

\frac{2 cos ( \frac{x}{3} )}{2} = \frac{2}{2}

Simplify

cos (\frac{x}{3}) = \frac{2}{2}

cos (\frac{x}{3}) = \frac{2}{2}

General solutions for

cos (\frac{x}{3}) = \frac{2}{2}

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}

\frac{x}{3} = \frac{π}{4} + 2 πn, \frac{x}{3} = \frac{7 π}{4} + 2 πn

\frac{x}{3} = \frac{π}{4} + 2 πn, \frac{x}{3} = \frac{7 π}{4} + 2 πn

Solve

\frac{x}{3} = \frac{π}{4} + 2 πn : x = \frac{3 π}{4} + 6 πn

\frac{x}{3} = \frac{π}{4} + 2 πn

Multiply both sides by

3

\frac{x}{3} = \frac{π}{4} + 2 πn

Multiply both sides by

3

\frac{3 x}{3} = 3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} = 3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

3 \cdot \frac{π}{4} + 3 \cdot 2 πn : \frac{3 π}{4} + 6 πn

3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Multiply

3 \cdot \frac{π}{4} : \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 3}{4}

= \frac{3 π}{4} + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= \frac{3 π}{4} + 6 πn

x = \frac{3 π}{4} + 6 πn

x = \frac{3 π}{4} + 6 πn

x = \frac{3 π}{4} + 6 πn

Solve

\frac{x}{3} = \frac{7 π}{4} + 2 πn : x = \frac{21 π}{4} + 6 πn

\frac{x}{3} = \frac{7 π}{4} + 2 πn

Multiply both sides by

3

\frac{x}{3} = \frac{7 π}{4} + 2 πn

Multiply both sides by

3

\frac{3 x}{3} = 3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} = 3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn : \frac{21 π}{4} + 6 πn

3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

3 \cdot \frac{7 π}{4} = \frac{21 π}{4}

3 \cdot \frac{7 π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 π 3}{4}

Multiply the numbers:

7 \cdot 3 = 21

= \frac{21 π}{4}

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 6 πn

= \frac{21 π}{4} + 6 πn

x = \frac{21 π}{4} + 6 πn

x = \frac{21 π}{4} + 6 πn

x = \frac{21 π}{4} + 6 πn

x = \frac{3 π}{4} + 6 πn, x = \frac{21 π}{4} + 6 πn

Popular Examples

tan(2x)-tan(x)=0

tan (2 x) - tan (x) = 0

cot(θ)=sqrt(3)

cot (θ) = 3

sin(x)=0.7

sin (x) = 0.7

sin(x)=(-sqrt(3))/2

sin (x) = \frac{- 3}{2}

sin(x/2)=sqrt(3)-sin(x/2)

sin (\frac{x}{2}) = 3 - sin (\frac{x}{2})

Frequently Asked Questions (FAQ)

What is the general solution for 2cos(x/3)-sqrt(2)=0 ?
The general solution for 2cos(x/3)-sqrt(2)=0 is x=(3pi)/4+6pin,x=(21pi)/4+6pin