What is the general solution for sec(x)=-3 ?

The general solution for sec(x)=-3 is x=1.91063…+2pin,x=-1.91063…+2pin

sec(x)=-3

sec (x) = - 3

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Degrees

x = 109.47122 \dots^{\circ} + 36 0^{\circ} n, x = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sec (x) = - 3

Apply trig inverse properties

sec (x) = - 3

General solutions for

sec (x) = - 3

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

Show solutions in decimal form

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

2 tan (x) csc (x) + 2 csc (x) + tan (x) + 1 = 0

csc (x) + cot (x) = 3, 0 \leq x \leq 2 π

(tan^{2} (x) - 4) (2 cos (x) + 1) = 0

cos (a) = \frac{1}{4}

sin (x) = 0.55

What is the general solution for sec(x)=-3 ?
The general solution for sec(x)=-3 is x=1.91063…+2pin,x=-1.91063…+2pin