What is the general solution for cos(θ)= 2/(sqrt(13)) ?

The general solution for cos(θ)= 2/(sqrt(13)) is θ=0.98279…+2pin,θ=2pi-0.98279…+2pin

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cos(θ)= 2/(sqrt(13))

cos (θ) = \frac{2}{13}

θ = 0.98279 \dots + 2 πn, θ = 2 π - 0.98279 \dots + 2 πn

Solution steps

cos (θ) = \frac{2}{13}

Simplify

\frac{2}{13} : \frac{2 13}{13}

Apply trig inverse properties

θ = arccos (\frac{2 13}{13}) + 2 πn, θ = 2 π - arccos (\frac{2 13}{13}) + 2 πn

Show solutions in decimal form

θ = 0.98279 \dots + 2 πn, θ = 2 π - 0.98279 \dots + 2 πn

4 sin (x - π) + 2 = 0

\frac{1}{2} tan (2 x) = tan (x)

sin (x + π) + cos (x + π) = 0

2 sin^{2} (x) - 3 sin (x) = - 1, 0 \leq x \leq 2 π

5 cos (x) + 23 = cos (x)

What is the general solution for cos(θ)= 2/(sqrt(13)) ?
The general solution for cos(θ)= 2/(sqrt(13)) is θ=0.98279…+2pin,θ=2pi-0.98279…+2pin