What is the general solution for 5sec(θ)-6=0 ?

The general solution for 5sec(θ)-6=0 is θ=0.58568…+2pin,θ=2pi-0.58568…+2pin

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5sec(θ)-6=0

5 sec (θ) - 6 = 0

θ = 0.58568 \dots + 2 πn, θ = 2 π - 0.58568 \dots + 2 πn

Degrees

θ = 33.55730 \dots^{\circ} + 36 0^{\circ} n, θ = 326.44269 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sec (θ) - 6 = 0

Move

6

to the right side

5 sec (θ) - 6 = 0

Add

6

to both sides

5 sec (θ) - 6 + 6 = 0 + 6

Simplify

5 sec (θ) = 6

5 sec (θ) = 6

Divide both sides by

5

5 sec (θ) = 6

Divide both sides by

5

\frac{5 sec ( θ )}{5} = \frac{6}{5}

Simplify

sec (θ) = \frac{6}{5}

sec (θ) = \frac{6}{5}

Apply trig inverse properties

sec (θ) = \frac{6}{5}

General solutions for

sec (θ) = \frac{6}{5}

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

θ = arcsec (\frac{6}{5}) + 2 πn, θ = 2 π - arcsec (\frac{6}{5}) + 2 πn

θ = arcsec (\frac{6}{5}) + 2 πn, θ = 2 π - arcsec (\frac{6}{5}) + 2 πn

Show solutions in decimal form

θ = 0.58568 \dots + 2 πn, θ = 2 π - 0.58568 \dots + 2 πn

sec (x) = - 1, - 2 π \leq x \leq 2 π

sin^{2} (x) - cos^{2} (x) + cos (x) = 0, 0 \leq x \leq 2 π

\frac{1}{cos ( 2 x )} + tan (2 x) = 3 cos (2 x)

tan (θ) = - 24

tan^{2} (θ) + 5 tan (θ) + 2 = 0

What is the general solution for 5sec(θ)-6=0 ?
The general solution for 5sec(θ)-6=0 is θ=0.58568…+2pin,θ=2pi-0.58568…+2pin