What is the general solution for sec(θ)+3=0 ?

The general solution for sec(θ)+3=0 is θ=1.91063…+2pin,θ=-1.91063…+2pin

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sec(θ)+3=0

sec (θ) + 3 = 0

θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

Degrees

θ = 109.47122 \dots^{\circ} + 36 0^{\circ} n, θ = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sec (θ) + 3 = 0

Move

3

to the right side

sec (θ) + 3 = 0

Subtract

3

from both sides

sec (θ) + 3 - 3 = 0 - 3

Simplify

sec (θ) = - 3

sec (θ) = - 3

Apply trig inverse properties

sec (θ) = - 3

General solutions for

sec (θ) = - 3

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

Show solutions in decimal form

θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

2 sin (x) cos (x) + 3 sin (x) = 0

cos (2 x) - cos (x) = 0, 0 \leq x < 2 π

x, 2 cos (2 x) - 1 = 0

tan (θ) + 12 = 2 tan (θ) + 11

8 sin (x) = 8 tan (x)

What is the general solution for sec(θ)+3=0 ?
The general solution for sec(θ)+3=0 is θ=1.91063…+2pin,θ=-1.91063…+2pin