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

The general solution for 3cos(θ)=2 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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3cos(θ)=2

3 cos (θ) = 2

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

Degrees

θ = 48.18968 \dots^{\circ} + 36 0^{\circ} n, θ = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (θ) = 2

Divide both sides by

3

3 cos (θ) = 2

Divide both sides by

3

\frac{3 cos ( θ )}{3} = \frac{2}{3}

Simplify

cos (θ) = \frac{2}{3}

cos (θ) = \frac{2}{3}

Apply trig inverse properties

cos (θ) = \frac{2}{3}

General solutions for

cos (θ) = \frac{2}{3}

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

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

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

Show solutions in decimal form

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

cot (t) = - \frac{1}{3}

sin (2 x) = - 2 sin (x)

cos (x) = - \frac{31}{52019}

csc (\frac{x}{4}) = 2

4 cos (θ) = sec (θ)

What is the general solution for 3cos(θ)=2 ?
The general solution for 3cos(θ)=2 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin