What is the general solution for 7sec(θ)+9=-5 ?

The general solution for 7sec(θ)+9=-5 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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7sec(θ)+9=-5

7 sec (θ) + 9 = - 5

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

7 sec (θ) + 9 = - 5

Move

9

to the right side

7 sec (θ) + 9 = - 5

Subtract

9

from both sides

7 sec (θ) + 9 - 9 = - 5 - 9

Simplify

7 sec (θ) = - 14

7 sec (θ) = - 14

Divide both sides by

7

7 sec (θ) = - 14

Divide both sides by

7

\frac{7 sec ( θ )}{7} = \frac{- 14}{7}

Simplify

\frac{7 sec ( θ )}{7} = \frac{- 14}{7}

Simplify

\frac{7 sec ( θ )}{7} : sec (θ)

\frac{7 sec ( θ )}{7}

Divide the numbers:

\frac{7}{7} = 1

= sec (θ)

Simplify

\frac{- 14}{7} : - 2

\frac{- 14}{7}

Apply the fraction rule:

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

= - \frac{14}{7}

Divide the numbers:

\frac{14}{7} = 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

1 - 3 cos (x) = sin^{2} (x)

15 sec^{2} (x) - 20 = 0

1 - 2 tan^{2} (x) = - tan^{2} (x)

sin (x) = - \frac{1}{2}, 0 \leq x \leq 2 π

sin^{2} (x) + 2 - cos^{2} (x) = 3 sin (x)

What is the general solution for 7sec(θ)+9=-5 ?
The general solution for 7sec(θ)+9=-5 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin