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

The general solution for sec(θ)=4 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin

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sec(θ)=4

sec (θ) = 4

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

Solution steps

sec (θ) = 4

Apply trig inverse properties

θ = arcsec (4) + 2 πn, θ = 2 π - arcsec (4) + 2 πn

Show solutions in decimal form

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

- sin (x) - sin^{2} (x) + cos^{2} (x) = 0

5 sin (x) = 1

5 sin (x) = 5

(1 + sin (x)) (1 + sin (x)) = cos^{2} (x)

cos (θ) = - 0.866

What is the general solution for sec(θ)=4 ?
The general solution for sec(θ)=4 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin