What is the general solution for cos(θ)= 6/(3sqrt(5)) ?

The general solution for cos(θ)= 6/(3sqrt(5)) is θ=0.46364…+2pin,θ=2pi-0.46364…+2pin

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cos(θ)= 6/(3sqrt(5))

cos (θ) = \frac{6}{3 5}

θ = 0.46364 \dots + 2 πn, θ = 2 π - 0.46364 \dots + 2 πn

Radians

θ = 0.46364 \dots + 6.28318 \dots n, θ = 5.81953 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{6}{3 5}

Simplify

\frac{6}{3 5} : \frac{2 5}{5}

\frac{6}{3 5}

Divide the numbers:

\frac{6}{3} = 2

= \frac{2}{5}

Rationalize

\frac{2}{5} : \frac{2 5}{5}

\frac{2}{5}

Multiply by the conjugate

\frac{5}{5}

= \frac{2 5}{5 5}

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= \frac{2 5}{5}

= \frac{2 5}{5}

cos (θ) = \frac{2 5}{5}

Apply trig inverse properties

cos (θ) = \frac{2 5}{5}

General solutions for

cos (θ) = \frac{2 5}{5}

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

θ = arccos (\frac{2 5}{5}) + 2 πn, θ = 2 π - arccos (\frac{2 5}{5}) + 2 πn

θ = arccos (\frac{2 5}{5}) + 2 πn, θ = 2 π - arccos (\frac{2 5}{5}) + 2 πn

Show solutions in decimal form

θ = 0.46364 \dots + 2 πn, θ = 2 π - 0.46364 \dots + 2 πn

3 cos (x) = 2 cos^{2} (x)

4 sin (x) cos (x) - 2 cos (x) + 2 sin (x) - 1 = 0

tan (2 x) = 2 cot (2 x)

tan (x) = - 0.74

sec (A) = \frac{8}{2}

What is the general solution for cos(θ)= 6/(3sqrt(5)) ?
The general solution for cos(θ)= 6/(3sqrt(5)) is θ=0.46364…+2pin,θ=2pi-0.46364…+2pin