What is the general solution for 3-3cos(5x)=3cos(5x) ?

The general solution for 3-3cos(5x)=3cos(5x) is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

3-3cos(5x)=3cos(5x)

Solution

3 - 3 cos (5 x) = 3 cos (5 x)

Solution

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Degrees

x = 1 2^{\circ} + 7 2^{\circ} n, x = 6 0^{\circ} + 7 2^{\circ} n

Solution steps

3 - 3 cos (5 x) = 3 cos (5 x)

Solve by substitution

3 - 3 cos (5 x) = 3 cos (5 x)

Let:

cos (5 x) = u

3 - 3 u = 3 u

3 - 3 u = 3 u : u = \frac{1}{2}

3 - 3 u = 3 u

Move

3

to the right side

3 - 3 u = 3 u

Subtract

3

from both sides

3 - 3 u - 3 = 3 u - 3

Simplify

- 3 u = 3 u - 3

- 3 u = 3 u - 3

Move

3 u

to the left side

- 3 u = 3 u - 3

Subtract

3 u

from both sides

- 3 u - 3 u = 3 u - 3 - 3 u

Simplify

- 6 u = - 3

- 6 u = - 3

Divide both sides by

- 6

- 6 u = - 3

Divide both sides by

- 6

\frac{- 6 u}{- 6} = \frac{- 3}{- 6}

Simplify

\frac{- 6 u}{- 6} = \frac{- 3}{- 6}

Simplify

\frac{- 6 u}{- 6} : u

\frac{- 6 u}{- 6}

Apply the fraction rule:

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

= \frac{6 u}{6}

Divide the numbers:

\frac{6}{6} = 1

= u

Simplify

\frac{- 3}{- 6} : \frac{1}{2}

\frac{- 3}{- 6}

Apply the fraction rule:

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

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

Substitute back

u = cos (5 x)

cos (5 x) = \frac{1}{2}

cos (5 x) = \frac{1}{2}

cos (5 x) = \frac{1}{2} : x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

cos (5 x) = \frac{1}{2}

General solutions for

cos (5 x) = \frac{1}{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}

5 x = \frac{π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

5 x = \frac{π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

Solve

5 x = \frac{π}{3} + 2 πn : x = \frac{π}{15} + \frac{2 πn}{5}

5 x = \frac{π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{π}{3} + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5} : \frac{π}{15} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} = \frac{π}{15}

\frac{\frac{π}{3}}{5}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{π}{15}

= \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

Solve

5 x = \frac{5 π}{3} + 2 πn : x = \frac{π}{3} + \frac{2 πn}{5}

5 x = \frac{5 π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{5 π}{3} + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5} : \frac{π}{3} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} = \frac{π}{3}

\frac{\frac{5 π}{3}}{5}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{5 π}{15}

Cancel the common factor:

5

= \frac{π}{3}

= \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Combine all the solutions

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Graph

Popular Examples

1/(1-cos(x))+1/(1+cos(x))=2sec^2(x)

2cos^2(θ)-sin(θ)=2

cos(a)=(57)/(sqrt(113)*\sqrt{78)}

tan^2(x)+tan(x)-12=2

sin(o)= 3/5

Frequently Asked Questions (FAQ)

What is the general solution for 3-3cos(5x)=3cos(5x) ?
The general solution for 3-3cos(5x)=3cos(5x) is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5