What is the general solution for sec(θ)= 3/2 ?

The general solution for sec(θ)= 3/2 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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sec(θ)= 3/2

sec (θ) = \frac{3}{2}

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

Degrees

θ = 48.18968 \dots^{\circ} + 36 0^{\circ} n, θ = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sec (θ) = \frac{3}{2}

Apply trig inverse properties

sec (θ) = \frac{3}{2}

General solutions for

sec (θ) = \frac{3}{2}

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

θ = arcsec (\frac{3}{2}) + 2 πn, θ = 2 π - arcsec (\frac{3}{2}) + 2 πn

θ = arcsec (\frac{3}{2}) + 2 πn, θ = 2 π - arcsec (\frac{3}{2}) + 2 πn

Show solutions in decimal form

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

6 cos (θ) + 3 = 0

sin^{2} (x) + 5 sin (x) + 6 = 0

- 6 tan^{2} (θ) + 11 tan (θ) - 6 = - 2 tan (θ)

(sin (x) + 1)^{2} + cos^{2} (x) = 2

12 sin^{2} (x) - cos (x) - 6 = 0

What is the general solution for sec(θ)= 3/2 ?
The general solution for sec(θ)= 3/2 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin