What is the general solution for 2sec(θ)=6 ?

The general solution for 2sec(θ)=6 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin

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2sec(θ)=6

2 sec (θ) = 6

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

Degrees

θ = 70.52877 \dots^{\circ} + 36 0^{\circ} n, θ = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sec (θ) = 6

Divide both sides by

2

2 sec (θ) = 6

Divide both sides by

2

\frac{2 sec ( θ )}{2} = \frac{6}{2}

Simplify

sec (θ) = 3

sec (θ) = 3

Apply trig inverse properties

sec (θ) = 3

General solutions for

sec (θ) = 3

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

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

sin (2 x + 20) - 1 = \frac{- 1}{2}

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

0 = 4 + 3 cos (θ)

cos (θ) = \frac{6}{8}

x, 4 cos (x) \cdot sin (y) = 1

What is the general solution for 2sec(θ)=6 ?
The general solution for 2sec(θ)=6 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin