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

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

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sec(a)=-2

sec (a) = - 2

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

Degrees

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

Solution steps

sec (a) = - 2

General solutions for

sec (a) = - 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}

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

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

tan^{2} (γ) + 1 = cos^{2} (γ)

sin^{2} (x) + 8 sin (x) - 9 = 0

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ), 0^{\circ} \leq θ < 36 0^{\circ}

cot^{2} (θ) + 4 csc (θ) = - 5

10 sin (a) + 7 sin (a) + 1 sin (a) + 8 sin (a) = 48

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