What is the general solution for sec(x)=2 ?

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

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sec(x)=2

sec (x) = 2

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

sec (x) = 2

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{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (\frac{13 π}{12})

sin (x) + cos (x) = 0

tan (- \frac{2 π}{3})

sec (θ) - 2 = 0

sin (θ) sin (2 θ) = 0, 0 \leq θ \leq 2 π

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