What is the general solution for sec(θ)= 1/(cos(67.38)) ?

The general solution for sec(θ)= 1/(cos(67.38)) is θ=1.17600…+360n,θ=360-1.17600…+360n

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sec(θ)= 1/(cos(67.38))

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

θ = 1.17600 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.17600 \dots + 36 0^{\circ} n

Radians

θ = 1.17600 \dots + 2 πn, θ = 2 π - 1.17600 \dots + 2 πn

Solution steps

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

Apply trig inverse properties

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

General solutions for

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

θ = arcsec (\frac{1}{cos ( 67.3 8 ^{\circ} )}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arcsec (\frac{1}{cos ( 67.3 8 ^{\circ} )}) + 36 0^{\circ} n

θ = arcsec (\frac{1}{cos ( 67.3 8 ^{\circ} )}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arcsec (\frac{1}{cos ( 67.3 8 ^{\circ} )}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 1.17600 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.17600 \dots + 36 0^{\circ} n

x, 6 cos^{2} (x) + cos (x) - 1 = 0

3 = tan (\frac{θ}{3})

sec (x) - 2 = 0, 0 \leq x < 2 π

cos (x) = \frac{15}{19}

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

What is the general solution for sec(θ)= 1/(cos(67.38)) ?
The general solution for sec(θ)= 1/(cos(67.38)) is θ=1.17600…+360n,θ=360-1.17600…+360n