What is the general solution for sec^2(θ)+5sec(θ)-6=0 ?

The general solution for sec^2(θ)+5sec(θ)-6=0 is θ=2pin,θ=1.73824…+2pin,θ=-1.73824…+2pin

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sec^2(θ)+5sec(θ)-6=0

sec^{2} (θ) + 5 sec (θ) - 6 = 0

θ = 2 πn, θ = 1.73824 \dots + 2 πn, θ = - 1.73824 \dots + 2 πn

Solution steps

sec^{2} (θ) + 5 sec (θ) - 6 = 0

Solve by substitution

sec (θ) = 1, sec (θ) = - 6

sec (θ) = 1 : θ = 2 πn

sec (θ) = - 6 : θ = arcsec (- 6) + 2 πn, θ = - arcsec (- 6) + 2 πn

Combine all the solutions

θ = 2 πn, θ = arcsec (- 6) + 2 πn, θ = - arcsec (- 6) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = 1.73824 \dots + 2 πn, θ = - 1.73824 \dots + 2 πn

cos (x) = 0.75

cos (x) = 0.76

0 = 4 cos (2 x)

cos (x) + 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

82 cos (θ) + 6 = - 2

What is the general solution for sec^2(θ)+5sec(θ)-6=0 ?
The general solution for sec^2(θ)+5sec(θ)-6=0 is θ=2pin,θ=1.73824…+2pin,θ=-1.73824…+2pin