What is the general solution for cos(θ)= 8/12 ?

The general solution for cos(θ)= 8/12 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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cos(θ)= 8/12

cos (θ) = \frac{8}{12}

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

cos (θ) = \frac{8}{12}

Cancel the common factor:

4

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

sin (x) sin (2 x) = 0

sin (x) = 1.2

9 cos^{2} (θ) = - 10 cos (θ) - 1

3 sin (x) = 3 sin (2 x)

sin (x) + cos (2 x) = 0.75

What is the general solution for cos(θ)= 8/12 ?
The general solution for cos(θ)= 8/12 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin