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

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

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2=sec(x)

2 = sec (x)

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

2 = sec (x)

Switch sides

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{x}{2} - \frac{π}{3}) = \frac{1}{2}

2 tan (x) + sec (x) = 0, 0 \leq x < 2 π

1 - sin (x) = 3 cos (x)

cos (x) - sec (x) = 0

2 + 7 cos (x) = 4 sin^{2} (x)

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