What is the general solution for cos(θ)=-4/9 ?

The general solution for cos(θ)=-4/9 is θ=2.03135…+2pin,θ=-2.03135…+2pin

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cos(θ)=-4/9

cos (θ) = - \frac{4}{9}

θ = 2.03135 \dots + 2 πn, θ = - 2.03135 \dots + 2 πn

Degrees

θ = 116.38779 \dots^{\circ} + 36 0^{\circ} n, θ = - 116.38779 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = - \frac{4}{9}

Apply trig inverse properties

cos (θ) = - \frac{4}{9}

General solutions for

cos (θ) = - \frac{4}{9}

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

θ = arccos (- \frac{4}{9}) + 2 πn, θ = - arccos (- \frac{4}{9}) + 2 πn

θ = arccos (- \frac{4}{9}) + 2 πn, θ = - arccos (- \frac{4}{9}) + 2 πn

Show solutions in decimal form

θ = 2.03135 \dots + 2 πn, θ = - 2.03135 \dots + 2 πn

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

2 cos^{2} (x) - 4 cos (x) + 2 = 0

cos^{2} (x) - sin^{2} (x) = 1 - 2 sin (x)

cos (x) = - 0.34

2 sin^{2} (x) = 3 sin (x) - 1

What is the general solution for cos(θ)=-4/9 ?
The general solution for cos(θ)=-4/9 is θ=2.03135…+2pin,θ=-2.03135…+2pin