What is the general solution for 17cos(x)+9=-cos(x) ?

The general solution for 17cos(x)+9=-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 Trigonometry >

17cos(x)+9=-cos(x)

Solution

17 cos (x) + 9 = - 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

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

Solve by substitution

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

Let:

cos (x) = u

17 u + 9 = - u

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

17 u + 9 = - u

Move

9

to the right side

17 u + 9 = - u

Subtract

9

from both sides

17 u + 9 - 9 = - u - 9

Simplify

17 u = - u - 9

17 u = - u - 9

Move

u

to the left side

17 u = - u - 9

Add

u

to both sides

17 u + u = - u - 9 + u

Simplify

18 u = - 9

18 u = - 9

Divide both sides by

18

18 u = - 9

Divide both sides by

18

\frac{18 u}{18} = \frac{- 9}{18}

Simplify

\frac{18 u}{18} = \frac{- 9}{18}

Simplify

\frac{18 u}{18} : u

\frac{18 u}{18}

Divide the numbers:

\frac{18}{18} = 1

= u

Simplify

\frac{- 9}{18} : - \frac{1}{2}

\frac{- 9}{18}

Apply the fraction rule:

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

= - \frac{9}{18}

Cancel the common factor:

9

= - \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

Graph

Popular Examples

(2cos(θ)+1)(cos(θ)-2)=0

(2 cos (θ) + 1) (cos (θ) - 2) = 0

4cos(2x)-1=1

4 cos (2 x) - 1 = 1

sin(2x)=cot(x)

sin (2 x) = cot (x)

cos(θ)=3

cos (θ) = 3

cos(θ)=4

cos (θ) = 4

Frequently Asked Questions (FAQ)

What is the general solution for 17cos(x)+9=-cos(x) ?
The general solution for 17cos(x)+9=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin