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

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

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sqrt(3)sec(x)=-2

3 sec (x) = - 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) = - 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

sec^{2} (x) = \frac{4}{3}

sin (θ) = \frac{3}{4}

3 tan (x) = 3

sin^{2} (θ) = \frac{1}{2}

1 + cos (θ) = 1 - sin (θ)

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