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

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

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sec(θ)=-3

sec (θ) = - 3

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

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

cos^{2} (x) - 5 cos (x) - 1 = 0

cos (2 θ) = - cos (θ)

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

2 cos^{2} (θ) = 1 - cos (θ)

- 5 cos^{2} (θ) = 12 sin (θ) + 4

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