What is the general solution for sec(x)=sqrt(4/3) ?

The general solution for sec(x)=sqrt(4/3) is x= pi/6+2pin,x=(11pi)/6+2pin

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sec(x)=sqrt(4/3)

sec (x) = \frac{4}{3}

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

Solution steps

sec (x) = \frac{4}{3}

Simplify

\frac{4}{3} : \frac{2 3}{3}

\frac{4}{3}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

Rationalize

\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}

= \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

cos (A) tan (A) = cos (A)

sin (x) = \frac{11 sin ( 12 0 ^{\circ} )}{18}

3 csc (θ) + 5 = csc (θ) + 9

\frac{cos ( 2 x )}{sin ( 3 x ) - sin ( x )} - 1 = 0

2 tan^{3} (x) - \frac{2}{3} tan (x) = 0, 0 \leq x \leq π

What is the general solution for sec(x)=sqrt(4/3) ?
The general solution for sec(x)=sqrt(4/3) is x= pi/6+2pin,x=(11pi)/6+2pin