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

The general solution for sec(x)=-sqrt(2) is x=(3pi)/4+2pin,x=(5pi)/4+2pin

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sec(x)=-sqrt(2)

sec (x) = - 2

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Degrees

x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

2 sin^{2} (θ) - cos (θ) = 1

3 sin^{2} (x) - 7 sin (x) + 2 = 0

tan (θ) = \frac{4}{3}

tan (x) = \frac{1}{3}

2 cos^{2} (θ) + cos (θ) - 1 = 0

What is the general solution for sec(x)=-sqrt(2) ?
The general solution for sec(x)=-sqrt(2) is x=(3pi)/4+2pin,x=(5pi)/4+2pin