What is the general solution for 2sec(θ)+4=0 ?

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

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2sec(θ)+4=0

2 sec (θ) + 4 = 0

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

2 sec (θ) + 4 = 0

Move

4

to the right side

2 sec (θ) + 4 = 0

Subtract

4

from both sides

2 sec (θ) + 4 - 4 = 0 - 4

Simplify

2 sec (θ) = - 4

2 sec (θ) = - 4

Divide both sides by

2

2 sec (θ) = - 4

Divide both sides by

2

\frac{2 sec ( θ )}{2} = \frac{- 4}{2}

Simplify

\frac{2 sec ( θ )}{2} = \frac{- 4}{2}

Simplify

\frac{2 sec ( θ )}{2} : sec (θ)

\frac{2 sec ( θ )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sec (θ)

Simplify

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

\frac{- 4}{2}

Apply the fraction rule:

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

= - \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 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

sin (x) = \frac{( 60 \cdot sin ( 15 5 ^{\circ} ) )}{97.72}

(1 - 2 cos (x)) (1 + sin (x)) = 0

3 cos (2 x) + 7 sin (x) - 5 = 0

cos^{2} (θ) = \frac{1}{3}

x, sin (\frac{x}{5}) = - \frac{3}{2}

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