What is the general solution for 3cos(θ)-2=0 ?

The general solution for 3cos(θ)-2=0 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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3cos(θ)-2=0

3 cos (θ) - 2 = 0

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

Solution steps

3 cos (θ) - 2 = 0

Move

2

to the right side

3 cos (θ) = 2

Divide both sides by

3

cos (θ) = \frac{2}{3}

Apply trig inverse properties

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

csc^{2} (\frac{x}{2}) + csc (\frac{x}{2}) = 4 + 4 sin (\frac{x}{2})

(cot (x) - 1) (sin (x) + 1) = 0

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

4 tan^{3} (x) - 12 tan (x) = 0

sin (x) = \frac{64}{80}

What is the general solution for 3cos(θ)-2=0 ?
The general solution for 3cos(θ)-2=0 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin