What is the general solution for 6sec(θ)+8=-4 ?

The general solution for 6sec(θ)+8=-4 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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6sec(θ)+8=-4

6 sec (θ) + 8 = - 4

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

Degrees

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

Solution steps

6 sec (θ) + 8 = - 4

Move

8

to the right side

6 sec (θ) + 8 = - 4

Subtract

8

from both sides

6 sec (θ) + 8 - 8 = - 4 - 8

Simplify

6 sec (θ) = - 12

6 sec (θ) = - 12

Divide both sides by

6

6 sec (θ) = - 12

Divide both sides by

6

\frac{6 sec ( θ )}{6} = \frac{- 12}{6}

Simplify

\frac{6 sec ( θ )}{6} = \frac{- 12}{6}

Simplify

\frac{6 sec ( θ )}{6} : sec (θ)

\frac{6 sec ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sec (θ)

Simplify

\frac{- 12}{6} : - 2

\frac{- 12}{6}

Apply the fraction rule:

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

= - \frac{12}{6}

Divide the numbers:

\frac{12}{6} = 2

= - 2

sec (θ) = - 2

sec (θ) = - 2

sec (θ) = - 2

General solutions for

sec (θ) = - 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}

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

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

cos^{2} (θ) - cos (θ) - 2 = 0

2 sin (3 x) = - 1

8 sin^{2} (θ) + 2 sin (θ) - 1 = 0

tan (θ) = 6

sin (4 x) = \frac{1}{2}

What is the general solution for 6sec(θ)+8=-4 ?
The general solution for 6sec(θ)+8=-4 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin