What is the general solution for sec((2pi)/3+x)=2 ?

The general solution for sec((2pi)/3+x)=2 is x=2pin-pi/3 ,x=2pin+pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec((2pi)/3+x)=2

Solution

sec (\frac{2 π}{3} + x) = 2

Solution

x = 2 πn - \frac{π}{3}, x = 2 πn + π

Degrees

x = - 6 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

sec (\frac{2 π}{3} + x) = 2

General solutions for

sec (\frac{2 π}{3} + x) = 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

Solve

\frac{2 π}{3} + x = \frac{π}{3} + 2 πn : x = 2 πn - \frac{π}{3}

\frac{2 π}{3} + x = \frac{π}{3} + 2 πn

Move

\frac{2 π}{3}

to the right side

\frac{2 π}{3} + x = \frac{π}{3} + 2 πn

Subtract

\frac{2 π}{3}

from both sides

\frac{2 π}{3} + x - \frac{2 π}{3} = \frac{π}{3} + 2 πn - \frac{2 π}{3}

Simplify

\frac{2 π}{3} + x - \frac{2 π}{3} = \frac{π}{3} + 2 πn - \frac{2 π}{3}

Simplify

\frac{2 π}{3} + x - \frac{2 π}{3} : x

\frac{2 π}{3} + x - \frac{2 π}{3}

Add similar elements:

\frac{2 π}{3} - \frac{2 π}{3} = 0

= x

Simplify

\frac{π}{3} + 2 πn - \frac{2 π}{3} : 2 πn - \frac{π}{3}

\frac{π}{3} + 2 πn - \frac{2 π}{3}

Group like terms

= 2 πn + \frac{π}{3} - \frac{2 π}{3}

Combine the fractions

\frac{π}{3} - \frac{2 π}{3} : - \frac{π}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π - 2 π}{3}

Add similar elements:

π - 2 π = - π

= \frac{- π}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{π}{3}

= 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

Solve

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

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

Move

\frac{2 π}{3}

to the right side

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

Subtract

\frac{2 π}{3}

from both sides

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

Simplify

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

Simplify

\frac{2 π}{3} + x - \frac{2 π}{3} : x

\frac{2 π}{3} + x - \frac{2 π}{3}

Add similar elements:

\frac{2 π}{3} - \frac{2 π}{3} = 0

= x

Simplify

\frac{5 π}{3} + 2 πn - \frac{2 π}{3} : 2 πn + π

\frac{5 π}{3} + 2 πn - \frac{2 π}{3}

Group like terms

= 2 πn + \frac{5 π}{3} - \frac{2 π}{3}

Combine the fractions

\frac{5 π}{3} - \frac{2 π}{3} : π

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 π - 2 π}{3}

Add similar elements:

5 π - 2 π = 3 π

= \frac{3 π}{3}

Divide the numbers:

\frac{3}{3} = 1

= π

= 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn - \frac{π}{3}, x = 2 πn + π

Popular Examples

sin(t)= 7/9 ,sin(2t)

sin (t) = \frac{7}{9}, sin (2 t)

8/17 =sin(2x)

\frac{8}{17} = sin (2 x)

sec(2x)+tan(2x)=2

sec (2 x) + tan (2 x) = 2

sec(2x)+tan(2x)=9

sec (2 x) + tan (2 x) = 9

2+3cos^2(x)=sin^2(x)+4cos(x)

2 + 3 cos^{2} (x) = sin^{2} (x) + 4 cos (x)

Frequently Asked Questions (FAQ)

What is the general solution for sec((2pi)/3+x)=2 ?
The general solution for sec((2pi)/3+x)=2 is x=2pin-pi/3 ,x=2pin+pi