What is the general solution for 7cos(x)=2+5cos(x) ?

The general solution for 7cos(x)=2+5cos(x) is x=2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7cos(x)=2+5cos(x)

7 cos (x) = 2 + 5 cos (x)

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

7 cos (x) = 2 + 5 cos (x)

Solve by substitution

7 cos (x) = 2 + 5 cos (x)

Let:

cos (x) = u

7 u = 2 + 5 u

7 u = 2 + 5 u : u = 1

7 u = 2 + 5 u

Move

5 u

to the left side

7 u = 2 + 5 u

Subtract

5 u

from both sides

7 u - 5 u = 2 + 5 u - 5 u

Simplify

2 u = 2

2 u = 2

Divide both sides by

2

2 u = 2

Divide both sides by

2

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

Simplify

u = 1

u = 1

Substitute back

u = cos (x)

cos (x) = 1

cos (x) = 1

cos (x) = 1 : x = 2 πn

cos (x) = 1

General solutions for

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Combine all the solutions

x = 2 πn

cos (x) = 7

5 sin (θ) cos (θ) + 4 cos (θ) = 0

2 csc (x) + 4 = 0

2 sin (x) = 3, 0 \leq x \leq 2 π

x, z = arcsin (x + y)

What is the general solution for 7cos(x)=2+5cos(x) ?
The general solution for 7cos(x)=2+5cos(x) is x=2pin