What is the general solution for 3sec(θ)-2sqrt(3)=0 ?

The general solution for 3sec(θ)-2sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin

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3sec(θ)-2sqrt(3)=0

3 sec (θ) - 23 = 0

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) - 23 = 0

Move

23

to the right side

3 sec (θ) - 23 = 0

Add

23

to both sides

3 sec (θ) - 23 + 23 = 0 + 23

Simplify

3 sec (θ) = 23

3 sec (θ) = 23

Divide both sides by

3

3 sec (θ) = 23

Divide both sides by

3

\frac{3 sec ( θ )}{3} = \frac{2 3}{3}

Simplify

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

sin^{2} (θ) cos (θ) = cos (θ)

cos (3 0^{\circ} + x) = 276

3 sin (2 x) + cos (2 x) = 2 cos (2 x)

sin (x) = - sin (x) cos (x)

tan^{2} (\frac{x}{2}) = 1

What is the general solution for 3sec(θ)-2sqrt(3)=0 ?
The general solution for 3sec(θ)-2sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin