What is the general solution for cos(θ)= 5/13 ?

The general solution for cos(θ)= 5/13 is θ=1.17600…+2pin,θ=2pi-1.17600…+2pin

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cos(θ)= 5/13

cos (θ) = \frac{5}{13}

θ = 1.17600 \dots + 2 πn, θ = 2 π - 1.17600 \dots + 2 πn

Degrees

θ = 67.38013 \dots^{\circ} + 36 0^{\circ} n, θ = 292.61986 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{5}{13}

Apply trig inverse properties

cos (θ) = \frac{5}{13}

General solutions for

cos (θ) = \frac{5}{13}

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

θ = arccos (\frac{5}{13}) + 2 πn, θ = 2 π - arccos (\frac{5}{13}) + 2 πn

θ = arccos (\frac{5}{13}) + 2 πn, θ = 2 π - arccos (\frac{5}{13}) + 2 πn

Show solutions in decimal form

θ = 1.17600 \dots + 2 πn, θ = 2 π - 1.17600 \dots + 2 πn

8 cos^{2} (x) + 4 cos (x) - 4 = 0

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

1 - cos (x) = 0

2 sin (x) cos (x) = - 3 cos (x)

sin (\frac{x}{2}) = cos (\frac{x}{2})

What is the general solution for cos(θ)= 5/13 ?
The general solution for cos(θ)= 5/13 is θ=1.17600…+2pin,θ=2pi-1.17600…+2pin