What is the general solution for cos(θ)= 2/(3sqrt(38)) ?

The general solution for cos(θ)= 2/(3sqrt(38)) is θ=1.46243…+2pin,θ=2pi-1.46243…+2pin

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cos(θ)= 2/(3sqrt(38))

cos (θ) = \frac{2}{3 38}

θ = 1.46243 \dots + 2 πn, θ = 2 π - 1.46243 \dots + 2 πn

Solution steps

cos (θ) = \frac{2}{3 38}

Simplify

\frac{2}{3 38} : \frac{38}{57}

Apply trig inverse properties

θ = arccos (\frac{38}{57}) + 2 πn, θ = 2 π - arccos (\frac{38}{57}) + 2 πn

Show solutions in decimal form

θ = 1.46243 \dots + 2 πn, θ = 2 π - 1.46243 \dots + 2 πn

sec (x) cos (x) = sin (x)

tan (θ) - 1 - 2 = sec (θ)

3 cos (2 x) + 4 cos (4 x) - 5 = 0

cos (2 θ) = \frac{20}{29}

- 6 sin (3 x) = 0

What is the general solution for cos(θ)= 2/(3sqrt(38)) ?
The general solution for cos(θ)= 2/(3sqrt(38)) is θ=1.46243…+2pin,θ=2pi-1.46243…+2pin