What is the general solution for 3sec(x)=9 ?

The general solution for 3sec(x)=9 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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3sec(x)=9

3 sec (x) = 9

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) = 9

Divide both sides by

3

3 sec (x) = 9

Divide both sides by

3

\frac{3 sec ( x )}{3} = \frac{9}{3}

Simplify

sec (x) = 3

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

cos^{2} (x) + 2 cos (x) + 1 = 0, 0 \leq x \leq 2 π

x, sin (2 x) = \frac{1}{2}

- 4 sin (x) = - cos^{2} (x) + 4, 0 \leq x \leq 2 π

2 sin (θ) cos (θ) - cos (θ) = 0

sin (2 x) cot (x) = 0

What is the general solution for 3sec(x)=9 ?
The general solution for 3sec(x)=9 is x=1.23095…+2pin,x=2pi-1.23095…+2pin