What is the general solution for sec(x)=-5,pi<x<(3pi)/2 ?

The general solution for sec(x)=-5,pi<x<(3pi)/2 is x=-1.77215…+2pi

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sec(x)=-5,pi<x<(3pi)/2

sec (x) = - 5, π < x < \frac{3 π}{2}

x = - 1.77215 \dots + 2 π

Degrees

x = 258.46304 \dots^{\circ}

Solution steps

sec (x) = - 5, π < x < \frac{3 π}{2}

Apply trig inverse properties

sec (x) = - 5

General solutions for

sec (x) = - 5

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 5) + 2 πn, x = - arcsec (- 5) + 2 πn

x = arcsec (- 5) + 2 πn, x = - arcsec (- 5) + 2 πn

Solutions for the range

π < x < \frac{3 π}{2}

x = - arcsec (- 5) + 2 π

Show solutions in decimal form

x = - 1.77215 \dots + 2 π

sin (\frac{θ}{2}) = \frac{3}{5}

2 sin^{3} (t) + sin^{2} (t) - 2 sin (t) - 1 = 0

sin (x) = \frac{1}{5}, cos (x) > 0

2 sin^{2} (2 θ) = - 1 - 3 sin (2 θ)

6 cos (x) = 3

What is the general solution for sec(x)=-5,pi<x<(3pi)/2 ?
The general solution for sec(x)=-5,pi<x<(3pi)/2 is x=-1.77215…+2pi