What is the general solution for 3sec(x)=-6 ?

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

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3sec(x)=-6

3 sec (x) = - 6

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

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

3 sec (x) = - 6

Divide both sides by

3

3 sec (x) = - 6

Divide both sides by

3

\frac{3 sec ( x )}{3} = \frac{- 6}{3}

Simplify

\frac{3 sec ( x )}{3} = \frac{- 6}{3}

Simplify

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

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

Divide the numbers:

\frac{3}{3} = 1

= sec (x)

Simplify

\frac{- 6}{3} : - 2

\frac{- 6}{3}

Apply the fraction rule:

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

= - \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= - 2

sec (x) = - 2

sec (x) = - 2

sec (x) = - 2

General solutions for

sec (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}

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

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

x, cos (x + x y) = 2

tan (a) = - 1

cos^{2} (x) + 2 cos (x) = - 1

cot (x) (1 - cos^{2} (x)) = \frac{1}{2} sin^{2} (x)

(tan (x) - 1) (2 sin (x) - 1) = 0

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