What is the general solution for sec(x)= 25/7 ?

The general solution for sec(x)= 25/7 is x=1.28700…+2pin,x=2pi-1.28700…+2pin

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sec(x)= 25/7

sec (x) = \frac{25}{7}

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

Solution steps

sec (x) = \frac{25}{7}

Apply trig inverse properties

x = arcsec (\frac{25}{7}) + 2 πn, x = 2 π - arcsec (\frac{25}{7}) + 2 πn

Show solutions in decimal form

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

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

tan (θ) = \frac{- 3}{3}

csc (2 θ) = \frac{1}{2} (sec (θ)) (cos (θ))

sec^{2} (x) + 2 sec (x) - 8 = 0

3 cos^{2} (x) + 4 sin (x) - 4 = 0

What is the general solution for sec(x)= 25/7 ?
The general solution for sec(x)= 25/7 is x=1.28700…+2pin,x=2pi-1.28700…+2pin