What is the general solution for sec(θ)= 8/5 ?

The general solution for sec(θ)= 8/5 is θ=0.89566…+2pin,θ=2pi-0.89566…+2pin

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sec(θ)= 8/5

sec (θ) = \frac{8}{5}

θ = 0.89566 \dots + 2 πn, θ = 2 π - 0.89566 \dots + 2 πn

Degrees

θ = 51.31781 \dots^{\circ} + 36 0^{\circ} n, θ = 308.68218 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sec (θ) = \frac{8}{5}

Apply trig inverse properties

sec (θ) = \frac{8}{5}

General solutions for

sec (θ) = \frac{8}{5}

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

θ = arcsec (\frac{8}{5}) + 2 πn, θ = 2 π - arcsec (\frac{8}{5}) + 2 πn

θ = arcsec (\frac{8}{5}) + 2 πn, θ = 2 π - arcsec (\frac{8}{5}) + 2 πn

Show solutions in decimal form

θ = 0.89566 \dots + 2 πn, θ = 2 π - 0.89566 \dots + 2 πn

4 tan^{2} (x) = sec^{2} (x)

sec (θ) = - 1.5

cos (x) = \frac{1}{2} 3

sin (2 x - 1 0^{\circ}) = cos (x + 4 0^{\circ})

sec (θ) = - 37

What is the general solution for sec(θ)= 8/5 ?
The general solution for sec(θ)= 8/5 is θ=0.89566…+2pin,θ=2pi-0.89566…+2pin