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

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

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-2=sec(x)

- 2 = sec (x)

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

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 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{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

2 sin^{2} (x) + 4 sin (x) = 2 cos^{2} (x) + 1

y, sec^{2} (y) = x

tan (β) = \frac{1}{3}

cos (4 \cdot x) = - 1

3 + 2 cos (x) = 4 cos (\frac{x}{2})

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