What is the general solution for 2sec(x)-5=0 ?

The general solution for 2sec(x)-5=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin

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2sec(x)-5=0

2 sec (x) - 5 = 0

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

Degrees

x = 66.42182 \dots^{\circ} + 36 0^{\circ} n, x = 293.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sec (x) - 5 = 0

Move

5

to the right side

2 sec (x) - 5 = 0

Add

5

to both sides

2 sec (x) - 5 + 5 = 0 + 5

Simplify

2 sec (x) = 5

2 sec (x) = 5

Divide both sides by

2

2 sec (x) = 5

Divide both sides by

2

\frac{2 sec ( x )}{2} = \frac{5}{2}

Simplify

sec (x) = \frac{5}{2}

sec (x) = \frac{5}{2}

Apply trig inverse properties

sec (x) = \frac{5}{2}

General solutions for

sec (x) = \frac{5}{2}

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

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

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

Show solutions in decimal form

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

tan (a) + cot (a) = sec (a) cos (a)

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

cos (θ) = \frac{- 3}{13}

cos (x) = 0.84

cos (2 x) = \frac{( 4 k - 5 )}{10}

What is the general solution for 2sec(x)-5=0 ?
The general solution for 2sec(x)-5=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin