What is the general solution for 9cos(x)+5=-cos(x) ?

The general solution for 9cos(x)+5=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9cos(x)+5=-cos(x)

Solution

9 cos (x) + 5 = - cos (x)

Solution

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

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

9 cos (x) + 5 = - cos (x)

Solve by substitution

9 cos (x) + 5 = - cos (x)

Let:

cos (x) = u

9 u + 5 = - u

9 u + 5 = - u : u = - \frac{1}{2}

9 u + 5 = - u

Move

5

to the right side

9 u + 5 = - u

Subtract

5

from both sides

9 u + 5 - 5 = - u - 5

Simplify

9 u = - u - 5

9 u = - u - 5

Move

u

to the left side

9 u = - u - 5

Add

u

to both sides

9 u + u = - u - 5 + u

Simplify

10 u = - 5

10 u = - 5

Divide both sides by

10

10 u = - 5

Divide both sides by

10

\frac{10 u}{10} = \frac{- 5}{10}

Simplify

\frac{10 u}{10} = \frac{- 5}{10}

Simplify

\frac{10 u}{10} : u

\frac{10 u}{10}

Divide the numbers:

\frac{10}{10} = 1

= u

Simplify

\frac{- 5}{10} : - \frac{1}{2}

\frac{- 5}{10}

Apply the fraction rule:

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

= - \frac{5}{10}

Cancel the common factor:

5

= - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

Substitute back

u = cos (x)

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

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

General solutions for

cos (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}

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

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

Combine all the solutions

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

Popular Examples

sin(x)-sin(2x)=0,0<= x<= 2pi

sin (x) - sin (2 x) = 0, 0 \leq x \leq 2 π

tan(θ)= 1/4

tan (θ) = \frac{1}{4}

tan(θ)= 1/3

tan (θ) = \frac{1}{3}

sqrt(2)sec(x)+2=0

2 sec (x) + 2 = 0

6sin(θ)-3=0

6 sin (θ) - 3 = 0

Frequently Asked Questions (FAQ)

What is the general solution for 9cos(x)+5=-cos(x) ?
The general solution for 9cos(x)+5=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin