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

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

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sec(x)=3,(3pi)/2 <= x<= 2pi,sin(2x)

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π, sin (2 x)

x = 2 π - 1.23095 \dots

Degrees

x = 289.47122 \dots^{\circ}

Solution steps

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π, sin (2 x)

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

Solutions for the range

\frac{3 π}{2} \leq x \leq 2 π

x = 2 π - arcsec (3)

Show solutions in decimal form

x = 2 π - 1.23095 \dots

2 + 8 cos (θ) = - 1 + 2 cos (θ)

sin^{2} (x) + cos^{2} (x) + cos (x) = 0

2.5 = 10 sin (x)

4.797896 cos (0.568 x - 2.595) = 0

2 cos (x) - 1 = 2 cos (2 x)

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