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

The general solution for sec(x)=(-2sqrt(3))/3 is x=(5pi)/6+2pin,x=(7pi)/6+2pin

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

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

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Degrees

x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

sin^{2} (x) = cos (x) + cos^{2} (x)

6 sin^{2} (x) - sin (x) - 2 = 0

3 cos^{2} (x) - 8 cos (x) + 4 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

sin (x) = \frac{5}{25}

sin (x) cot (x) = - \frac{2}{2}

What is the general solution for sec(x)=(-2sqrt(3))/3 ?
The general solution for sec(x)=(-2sqrt(3))/3 is x=(5pi)/6+2pin,x=(7pi)/6+2pin