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

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

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sqrt(3)sec(θ)=2

3 sec (θ) = 2

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

3 sec (θ) = 2

Divide both sides by

3

3 sec (θ) = 2

Divide both sides by

3

\frac{3 sec ( θ )}{3} = \frac{2}{3}

Simplify

\frac{3 sec ( θ )}{3} = \frac{2}{3}

Simplify

\frac{3 sec ( θ )}{3} : sec (θ)

\frac{3 sec ( θ )}{3}

Cancel the common factor:

3

= sec (θ)

Simplify

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

sec (θ) = \frac{2 3}{3}

sec (θ) = \frac{2 3}{3}

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

cosh (x) = - 1

5 sin (2 θ) = 7 cos (2 θ)

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

sin (x) cos (x) = 2 cos (x)

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

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