What is the general solution for cos(θ)=(-1)/3 ?

The general solution for cos(θ)=(-1)/3 is θ=1.91063…+2pin,θ=-1.91063…+2pin

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cos(θ)=(-1)/3

cos (θ) = \frac{- 1}{3}

θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

Degrees

θ = 109.47122 \dots^{\circ} + 36 0^{\circ} n, θ = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

cos (θ) = - \frac{1}{3}

Apply trig inverse properties

cos (θ) = - \frac{1}{3}

General solutions for

cos (θ) = - \frac{1}{3}

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

θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

What is the general solution for cos(θ)=(-1)/3 ?
The general solution for cos(θ)=(-1)/3 is θ=1.91063…+2pin,θ=-1.91063…+2pin