What is the general solution for 2+2cos(2x)=0 ?

The general solution for 2+2cos(2x)=0 is x= pi/2+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

2+2cos(2x)=0

2 + 2 cos (2 x) = 0

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

2 + 2 cos (2 x) = 0

Move

2

to the right side

2 + 2 cos (2 x) = 0

Subtract

2

from both sides

2 + 2 cos (2 x) - 2 = 0 - 2

Simplify

2 cos (2 x) = - 2

2 cos (2 x) = - 2

Divide both sides by

2

2 cos (2 x) = - 2

Divide both sides by

2

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

Simplify

cos (2 x) = - 1

cos (2 x) = - 1

General solutions for

cos (2 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}

2 x = π + 2 πn

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Divide both sides by

2

2 x = π + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

csc (x) - 2 cot (x) = 0

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

cos^{2} (x) - sin (x) cos (x) = 0

x, 4 sin (x) + 2 = 0

- tan^{2} (x) - 2 tan (x) - 1 = 0

What is the general solution for 2+2cos(2x)=0 ?
The general solution for 2+2cos(2x)=0 is x= pi/2+pin