What is the general solution for 4sec(θ)+6=-2,0<= θ<2pi ?

The general solution for 4sec(θ)+6=-2,0<= θ<2pi is θ=(2pi)/3 ,θ=(4pi)/3

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4sec(θ)+6=-2,0<= θ<2pi

4 sec (θ) + 6 = - 2, 0 \leq θ < 2 π

θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

Degrees

θ = 12 0^{\circ}, θ = 24 0^{\circ}

Solution steps

4 sec (θ) + 6 = - 2, 0 \leq θ < 2 π

Move

6

to the right side

4 sec (θ) + 6 = - 2

Subtract

6

from both sides

4 sec (θ) + 6 - 6 = - 2 - 6

Simplify

4 sec (θ) = - 8

4 sec (θ) = - 8

Divide both sides by

4

4 sec (θ) = - 8

Divide both sides by

4

\frac{4 sec ( θ )}{4} = \frac{- 8}{4}

Simplify

\frac{4 sec ( θ )}{4} = \frac{- 8}{4}

Simplify

\frac{4 sec ( θ )}{4} : sec (θ)

\frac{4 sec ( θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sec (θ)

Simplify

\frac{- 8}{4} : - 2

\frac{- 8}{4}

Apply the fraction rule:

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

= - \frac{8}{4}

Divide the numbers:

\frac{8}{4} = 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

Solutions for the range

0 \leq θ < 2 π

θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

What is the general solution for 4sec(θ)+6=-2,0<= θ<2pi ?
The general solution for 4sec(θ)+6=-2,0<= θ<2pi is θ=(2pi)/3 ,θ=(4pi)/3