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

The general solution for 5cos(x)-sqrt(3)=3cos(x) is x= pi/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solve by substitution

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

Let:

cos (x) = u

5 u - 3 = 3 u

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

5 u - 3 = 3 u

Move

3

to the right side

5 u - 3 = 3 u

Add

3

to both sides

5 u - 3 + 3 = 3 u + 3

Simplify

5 u = 3 u + 3

5 u = 3 u + 3

Move

3 u

to the left side

5 u = 3 u + 3

Subtract

3 u

from both sides

5 u - 3 u = 3 u + 3 - 3 u

Simplify

2 u = 3

2 u = 3

Divide both sides by

2

2 u = 3

Divide both sides by

2

\frac{2 u}{2} = \frac{3}{2}

Simplify

u = \frac{3}{2}

u = \frac{3}{2}

Substitute back

u = cos (x)

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

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

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

General solutions for

cos (x) = \frac{3}{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{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

tan (x) + 3 = 0

2 sin (x) - 1 = 0

tan (x) = \frac{5}{3}

cos (\frac{x}{2}) \frac{1}{2} = 0

2 sin (x) + csc (x) = 3

What is the general solution for 5cos(x)-sqrt(3)=3cos(x) ?
The general solution for 5cos(x)-sqrt(3)=3cos(x) is x= pi/6+2pin,x=(11pi)/6+2pin