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

2 sin (θ) + 3 = - csc (θ)

2 sin (\frac{2 x}{3}) - 2 = 0

tan (θ) = - \frac{1}{4}

\frac{1}{cos ( x ) + 1} + \frac{1}{cos ( x ) - 1} = 2 csc (x) cot (x)

3 - sin (θ) = cos (2 θ)

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