What is the general solution for sec(θ)= 5/2 ?

The general solution for sec(θ)= 5/2 is θ=1.15927…+2pin,θ=2pi-1.15927…+2pin

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sec(θ)= 5/2

sec (θ) = \frac{5}{2}

θ = 1.15927 \dots + 2 πn, θ = 2 π - 1.15927 \dots + 2 πn

Solution steps

sec (θ) = \frac{5}{2}

Apply trig inverse properties

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

Show solutions in decimal form

θ = 1.15927 \dots + 2 πn, θ = 2 π - 1.15927 \dots + 2 πn

4 cos (2 x) = 2 - 8 cos (x)

tan (x) = \frac{7}{8}

4 cos^{2} (x) + 1 = 0

3 cos^{2} (x) - 2 cos (x) = 0

cos (x - \frac{π}{2}) = 0

What is the general solution for sec(θ)= 5/2 ?
The general solution for sec(θ)= 5/2 is θ=1.15927…+2pin,θ=2pi-1.15927…+2pin