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

The general solution for solvefor θ,sec(θ)=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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solvefor θ,sec(θ)=2

solve for

θ, sec (θ) = 2

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Degrees

θ = 6 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

sec (θ) = 2

General solutions for

sec (θ) = 2

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

2 cos (4 θ) = 0

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

6 - 2 sin (θ) - 8 sin^{2} (θ) = 0

cos (2 θ) = cos (3 θ)

θ, 2 sin (θ) = 1.5

What is the general solution for solvefor θ,sec(θ)=2 ?
The general solution for solvefor θ,sec(θ)=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin