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

The general solution for 3=sec(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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3=sec(x)

3 = sec (x)

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Degrees

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 = sec (x)

Switch sides

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 = 2 π - arcsec (a) + 2 πn

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

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

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

2 cos (2 x) = 1

2 csc^{2} (x) = 1 + cos (x)

6 arccos (5 x) = 5 π

sin (x) + sin (x) cot (x) = 0

arctan (θ) = 1

What is the general solution for 3=sec(x) ?
The general solution for 3=sec(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin