What is the general solution for sec(θ)= 5/4 ?

The general solution for sec(θ)= 5/4 is θ=0.64350…+2pin,θ=2pi-0.64350…+2pin

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sec(θ)= 5/4

sec (θ) = \frac{5}{4}

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

Solution steps

sec (θ) = \frac{5}{4}

Apply trig inverse properties

θ = arcsec (\frac{5}{4}) + 2 πn, θ = 2 π - arcsec (\frac{5}{4}) + 2 πn

Show solutions in decimal form

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

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

4 cos^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

2 sin^{2} (x) + cos (x) - 1 = 0, 0 \leq x \leq 2 π

sin (x) - tan (x) = cos (x) - 1

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

What is the general solution for sec(θ)= 5/4 ?
The general solution for sec(θ)= 5/4 is θ=0.64350…+2pin,θ=2pi-0.64350…+2pin