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

The general solution for cos(θ)= 1/3 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin

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cos(θ)= 1/3

cos (θ) = \frac{1}{3}

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

Degrees

θ = 70.52877 \dots^{\circ} + 36 0^{\circ} n, θ = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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 = 2 π - arccos (a) + 2 πn

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

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

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

4 sin^{2} (x) = 3, 0 \leq x \leq 2 π

3 sin (x) + 1 = sin (x)

cos (2 θ - \frac{π}{2}) = 1

- sin (2 x) + cos (x) = 0

3 csc^{2} (x) = 4

What is the general solution for cos(θ)= 1/3 ?
The general solution for cos(θ)= 1/3 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin