What is the general solution for cos(θ)= 2/(sqrt(6)) ?

The general solution for cos(θ)= 2/(sqrt(6)) is θ=0.61547…+2pin,θ=2pi-0.61547…+2pin

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cos(θ)= 2/(sqrt(6))

cos (θ) = \frac{2}{6}

θ = 0.61547 \dots + 2 πn, θ = 2 π - 0.61547 \dots + 2 πn

Radians

θ = 0.61547 \dots + 6.28318 \dots n, θ = 5.66770 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{2}{6}

Simplify

\frac{2}{6} : \frac{2}{3}

\frac{2}{6}

Factor

6 : 23

Factor

6 = 2 \cdot 3

= 2 \cdot 3

Apply radical rule:

= 23

= \frac{2}{2 3}

Cancel

\frac{2}{2 3} : \frac{2}{3}

\frac{2}{2 3}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}} 3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{2 ^{1 - \frac{1}{2}}}{3}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2 ^{\frac{1}{2}}}{3}

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{2}{3}

= \frac{2}{3}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \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 = 0.61547 \dots + 2 πn, θ = 2 π - 0.61547 \dots + 2 πn

2 \cdot cos^{2} (x) = 1

cos^{2} (x) = \frac{1}{6}

x, z = arccos (x + y)

3 tan (x) - 2 cot (x) = 5

tan (θ) = \frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}}

What is the general solution for cos(θ)= 2/(sqrt(6)) ?
The general solution for cos(θ)= 2/(sqrt(6)) is θ=0.61547…+2pin,θ=2pi-0.61547…+2pin