What is the general solution for sqrt(3)sec(x)+4=2 ?

The general solution for sqrt(3)sec(x)+4=2 is x=(5pi)/6+2pin,x=(7pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)sec(x)+4=2

3 sec (x) + 4 = 2

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Degrees

x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

3 sec (x) + 4 = 2

Move

4

to the right side

3 sec (x) + 4 = 2

Subtract

4

from both sides

3 sec (x) + 4 - 4 = 2 - 4

Simplify

3 sec (x) = - 2

3 sec (x) = - 2

Divide both sides by

3

3 sec (x) = - 2

Divide both sides by

3

\frac{3 sec ( x )}{3} = \frac{- 2}{3}

Simplify

\frac{3 sec ( x )}{3} = \frac{- 2}{3}

Simplify

\frac{3 sec ( x )}{3} : sec (x)

\frac{3 sec ( x )}{3}

Cancel the common factor:

3

= sec (x)

Simplify

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

\frac{- 2}{3}

Apply the fraction rule:

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

= - \frac{2}{3}

Rationalize

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

- \frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

sec (x) = - \frac{2 3}{3}

sec (x) = - \frac{2 3}{3}

sec (x) = - \frac{2 3}{3}

General solutions for

sec (x) = - \frac{2 3}{3}

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}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

6 cos^{3} (x) = 6 cos (x)

tan^{2} (θ) = 3, 0 \leq θ < 2 π

cos (x) - cos (2 x) = 2 cos (x)

1 + cos (x) = \frac{3 + 4 cos ( x )}{2}

tan (Θ) = 1.4, - 9 0^{\circ} <, Θ < 9 0^{\circ}

What is the general solution for sqrt(3)sec(x)+4=2 ?
The general solution for sqrt(3)sec(x)+4=2 is x=(5pi)/6+2pin,x=(7pi)/6+2pin