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

The general solution for sqrt(2)+2cos(x)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

2 + 2 cos (x) = 0

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Degrees

x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n

Solution steps

2 + 2 cos (x) = 0

Move

2

to the right side

2 + 2 cos (x) = 0

Subtract

2

from both sides

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

Simplify

2 cos (x) = - 2

2 cos (x) = - 2

Divide both sides by

2

2 cos (x) = - 2

Divide both sides by

2

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

Simplify

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

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

General solutions for

cos (x) = - \frac{2}{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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

2 sin (θ) sec (θ) = 4 sin (θ)

sec (x - \frac{π}{7}) cos (x - \frac{π}{7}) = sin (x - \frac{π}{7})

cos (x) = \frac{17}{28}

sec^{4} (x) - 4 sec^{2} (x) = 0

\frac{cos ( x )}{sec ( x )} - \frac{sin ( x )}{csc ( x )} = 1

What is the general solution for sqrt(2)+2cos(x)=0 ?
The general solution for sqrt(2)+2cos(x)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin