What is the general solution for 0=-4cos(3x)+2sqrt(2) ?

The general solution for 0=-4cos(3x)+2sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3

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0=-4cos(3x)+2sqrt(2)

Solution

0 = - 4 cos (3 x) + 22

Solution

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

Degrees

x = 1 5^{\circ} + 12 0^{\circ} n, x = 10 5^{\circ} + 12 0^{\circ} n

Solution steps

0 = - 4 cos (3 x) + 22

Switch sides

- 4 cos (3 x) + 22 = 0

Move

22

to the right side

- 4 cos (3 x) + 22 = 0

Subtract

22

from both sides

- 4 cos (3 x) + 22 - 22 = 0 - 22

Simplify

- 4 cos (3 x) = - 22

- 4 cos (3 x) = - 22

Divide both sides by

- 4

- 4 cos (3 x) = - 22

Divide both sides by

- 4

\frac{- 4 cos ( 3 x )}{- 4} = \frac{- 2 2}{- 4}

Simplify

\frac{- 4 cos ( 3 x )}{- 4} = \frac{- 2 2}{- 4}

Simplify

\frac{- 4 cos ( 3 x )}{- 4} : cos (3 x)

\frac{- 4 cos ( 3 x )}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4 cos ( 3 x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos (3 x)

Simplify

\frac{- 2 2}{- 4} : \frac{2}{2}

\frac{- 2 2}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 2}{4}

Cancel the common factor:

2

= \frac{2}{2}

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

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

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

General solutions for

cos (3 x) = \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}

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

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

Solve

3 x = \frac{π}{4} + 2 πn : x = \frac{π}{12} + \frac{2 πn}{3}

3 x = \frac{π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{π}{4} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3} : \frac{π}{12} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

Solve

3 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{12} + \frac{2 πn}{3}

3 x = \frac{7 π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{7 π}{4} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3} : \frac{7 π}{12} + \frac{2 πn}{3}

\frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{7 π}{4}}{3} = \frac{7 π}{12}

\frac{\frac{7 π}{4}}{3}

Apply the fraction rule:

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

= \frac{7 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{7 π}{12}

= \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 0=-4cos(3x)+2sqrt(2) ?
The general solution for 0=-4cos(3x)+2sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3