What is the general solution for sec(β)=3,(3pi)/2 <β<2pi ?

The general solution for sec(β)=3,(3pi)/2 <β<2pi is β=2pi-1.23095…

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sec(β)=3,(3pi)/2 <β<2pi

sec (β) = 3, \frac{3 π}{2} < β < 2 π

β = 2 π - 1.23095 \dots

Solution steps

sec (β) = 3, \frac{3 π}{2} < β < 2 π

Apply trig inverse properties

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

Solutions for the range

\frac{3 π}{2} < β < 2 π

β = 2 π - arcsec (3)

Show solutions in decimal form

β = 2 π - 1.23095 \dots

cos (x) = \frac{2.9}{3.2}

sin (θ) = \frac{3}{2}, 0 \leq θ < 2 π

cos (θ) sin (θ) - 3 cos (θ) = 0

\frac{3}{2} = cos (θ)

7 sin (7 x) = 0

What is the general solution for sec(β)=3,(3pi)/2 <β<2pi ?
The general solution for sec(β)=3,(3pi)/2 <β<2pi is β=2pi-1.23095…