What is the general solution for sec(x)+1=0 ?

The general solution for sec(x)+1=0 is x=pi+2pin

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sec(x)+1=0

sec (x) + 1 = 0

x = π + 2 πn

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

sec (x) + 1 = 0

Move

1

to the right side

sec (x) + 1 = 0

Subtract

1

from both sides

sec (x) + 1 - 1 = 0 - 1

Simplify

sec (x) = - 1

sec (x) = - 1

General solutions for

sec (x) = - 1

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 = π + 2 πn

x = π + 2 πn

sin (2 x) = - sin (x)

\frac{sin ( x )}{2} + \frac{sin ( x )}{3} = \frac{1}{4}

2 cos (x) sin (x) - cos (x) = 0

cos (θ) = \frac{2}{3}

0 = cos (x)

What is the general solution for sec(x)+1=0 ?
The general solution for sec(x)+1=0 is x=pi+2pin