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

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

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sec(x)=3

sec (x) = 3

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

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

- sin (x) = cos (x)

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

4 sin (θ) + 3 = 1

25 cot^{2} (θ) - 1 = 0

cos (a) = \frac{5}{13}

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