What is the general solution for sec(x)=-2,0<= x<= 2pi ?

The general solution for sec(x)=-2,0<= x<= 2pi is x=(2pi)/3 ,x=(4pi)/3

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sec(x)=-2,0<= x<= 2pi

sec (x) = - 2, 0 \leq x \leq 2 π

x = \frac{2 π}{3}, x = \frac{4 π}{3}

Degrees

x = 12 0^{\circ}, x = 24 0^{\circ}

Solution steps

sec (x) = - 2, 0 \leq x \leq 2 π

General solutions for

sec (x) = - 2

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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{2 π}{3}, x = \frac{4 π}{3}

What is the general solution for sec(x)=-2,0<= x<= 2pi ?
The general solution for sec(x)=-2,0<= x<= 2pi is x=(2pi)/3 ,x=(4pi)/3