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

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

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sec(y)=-2

sec (y) = - 2

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

Degrees

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

Solution steps

sec (y) = - 2

General solutions for

sec (y) = - 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}

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

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

- 1 + 2 sin^{2} (x) = 0

θ, y = - 2 + cos (3 θ)

cos (2 x) + 5 \cdot cos (x) = - 3

2 cos^{2} (x) - sin (x) - 2 = 0

8 sin (x) + 7 cos (x) = 1

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