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

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

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3sec(x)-2sqrt(3)=0

3 sec (x) - 23 = 0

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

Degrees

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

Solution steps

3 sec (x) - 23 = 0

Move

23

to the right side

3 sec (x) - 23 = 0

Add

23

to both sides

3 sec (x) - 23 + 23 = 0 + 23

Simplify

3 sec (x) = 23

3 sec (x) = 23

Divide both sides by

3

3 sec (x) = 23

Divide both sides by

3

\frac{3 sec ( x )}{3} = \frac{2 3}{3}

Simplify

sec (x) = \frac{2 3}{3}

sec (x) = \frac{2 3}{3}

General solutions for

sec (x) = \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}

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

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

2 cos (x) - 3 = - 5

sin (3 θ) - sin (θ) = cos (2 θ)

2 sin (x) + (2 - 3) = 3 csc (x)

tan^{2} (θ) + 4 sec (θ) = - 5

0 = tan (θ)

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