What is the general solution for 3sec(θ)-4=0 ?

The general solution for 3sec(θ)-4=0 is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin

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3sec(θ)-4=0

3 sec (θ) - 4 = 0

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

Degrees

θ = 41.40962 \dots^{\circ} + 36 0^{\circ} n, θ = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 sec (θ) - 4 = 0

Move

4

to the right side

3 sec (θ) - 4 = 0

Add

4

to both sides

3 sec (θ) - 4 + 4 = 0 + 4

Simplify

3 sec (θ) = 4

3 sec (θ) = 4

Divide both sides by

3

3 sec (θ) = 4

Divide both sides by

3

\frac{3 sec ( θ )}{3} = \frac{4}{3}

Simplify

sec (θ) = \frac{4}{3}

sec (θ) = \frac{4}{3}

Apply trig inverse properties

sec (θ) = \frac{4}{3}

General solutions for

sec (θ) = \frac{4}{3}

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

θ = arcsec (\frac{4}{3}) + 2 πn, θ = 2 π - arcsec (\frac{4}{3}) + 2 πn

θ = arcsec (\frac{4}{3}) + 2 πn, θ = 2 π - arcsec (\frac{4}{3}) + 2 πn

Show solutions in decimal form

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

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

cot (2 θ) = \frac{3}{4}

x, 0 = 4 - sec^{2} (x)

tan (x) = - \frac{4}{33}

2 cot^{2} (x) - 11 csc (x) = - 14

What is the general solution for 3sec(θ)-4=0 ?
The general solution for 3sec(θ)-4=0 is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin