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

The general solution for sec(x)=-5/3 is x=2.21429…+2pin,x=-2.21429…+2pin

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sec(x)=-5/3

sec (x) = - \frac{5}{3}

x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

Solution steps

sec (x) = - \frac{5}{3}

Apply trig inverse properties

x = arcsec (- \frac{5}{3}) + 2 πn, x = - arcsec (- \frac{5}{3}) + 2 πn

Show solutions in decimal form

x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

\frac{sin ( x )}{1 + cos ( x )} = sin (\frac{x}{2})

2 \cdot cos (\frac{x}{2}) - cos (x) = 1

2 sin (θ) cos (θ) + 2 sin (θ) - 2 cos (θ) sin (θ) = 0

2 sin (2 x) + 2 cos (x) = 0

cosh (x) = \frac{3}{2}

What is the general solution for sec(x)=-5/3 ?
The general solution for sec(x)=-5/3 is x=2.21429…+2pin,x=-2.21429…+2pin