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

The general solution for 2=2cos(pi+x) is x=2pin-pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2=2cos(pi+x)

2 = 2 cos (π + x)

x = 2 πn - π

Degrees

x = - 18 0^{\circ} + 36 0^{\circ} n

Solution steps

2 = 2 cos (π + x)

Switch sides

2 cos (π + x) = 2

Divide both sides by

2

2 cos (π + x) = 2

Divide both sides by

2

\frac{2 cos ( π + x )}{2} = \frac{2}{2}

Simplify

cos (π + x) = 1

cos (π + x) = 1

General solutions for

cos (π + 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}

π + x = 0 + 2 πn

π + x = 0 + 2 πn

Solve

π + x = 0 + 2 πn : x = 2 πn - π

π + x = 0 + 2 πn

0 + 2 πn = 2 πn

π + x = 2 πn

Move

π

to the right side

π + x = 2 πn

Subtract

π

from both sides

π + x - π = 2 πn - π

Simplify

x = 2 πn - π

x = 2 πn - π

x = 2 πn - π

cot (x) + csc (x) cos (x) = 2, cot (x)

- 4 cos (3 θ) = 1

960 = 480 (1 - cos (7.5 x))

8 = 8 tan (θ)

2 sin (2 x) - 3 cos (x) = 0

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