What is the general solution for cos(θ)= 1/(sqrt(6)) ?

The general solution for cos(θ)= 1/(sqrt(6)) is θ=1.15026…+2pin,θ=2pi-1.15026…+2pin

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cos(θ)= 1/(sqrt(6))

cos (θ) = \frac{1}{6}

θ = 1.15026 \dots + 2 πn, θ = 2 π - 1.15026 \dots + 2 πn

Radians

θ = 1.15026 \dots + 6.28318 \dots n, θ = 5.13292 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{1}{6}

Simplify

\frac{1}{6} : \frac{6}{6}

\frac{1}{6}

Multiply by the conjugate

\frac{6}{6}

= \frac{1 \cdot 6}{6 6}

1 \cdot 6 = 6

66 = 6

66

Apply radical rule:

a a = a

66 = 6

= 6

= \frac{6}{6}

cos (θ) = \frac{6}{6}

Apply trig inverse properties

cos (θ) = \frac{6}{6}

General solutions for

cos (θ) = \frac{6}{6}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

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

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

Show solutions in decimal form

θ = 1.15026 \dots + 2 πn, θ = 2 π - 1.15026 \dots + 2 πn

What is the general solution for cos(θ)= 1/(sqrt(6)) ?
The general solution for cos(θ)= 1/(sqrt(6)) is θ=1.15026…+2pin,θ=2pi-1.15026…+2pin