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

The general solution for (2sqrt(3))/3 =sec(θ) is θ= pi/6+2pin,θ=(11pi)/6+2pin

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(2sqrt(3))/3 =sec(θ)

\frac{2 3}{3} = sec (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{2 3}{3} = sec (θ)

Switch sides

sec (θ) = \frac{2 3}{3}

General solutions for

sec (θ) = \frac{2 3}{3}

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}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

4 (sin (x))^{2} - 15 sin (x) - 4 = 0

1 + sin (θ) = 1 + sin (- θ)

cos (2 x) = 2 + 3 sin (x), \frac{π}{2} \leq x \leq \frac{3 π}{2}

tan (θ) = (\frac{3}{8})

29 = \frac{1}{2} (5.6) (7.1) sin (x)

What is the general solution for (2sqrt(3))/3 =sec(θ) ?
The general solution for (2sqrt(3))/3 =sec(θ) is θ= pi/6+2pin,θ=(11pi)/6+2pin