What is the general solution for cos(θ)=(11)/(sqrt(130)) ?

The general solution for cos(θ)=(11)/(sqrt(130)) is θ=0.26625…+2pin,θ=2pi-0.26625…+2pin

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cos(θ)=(11)/(sqrt(130))

cos (θ) = \frac{11}{130}

θ = 0.26625 \dots + 2 πn, θ = 2 π - 0.26625 \dots + 2 πn

Radians

θ = 0.26625 \dots + 6.28318 \dots n, θ = 6.01693 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{11}{130}

Simplify

\frac{11}{130} : \frac{11 130}{130}

\frac{11}{130}

Multiply by the conjugate

\frac{130}{130}

= \frac{11 130}{130 130}

130130 = 130

130130

Apply radical rule:

a a = a

130130 = 130

= 130

= \frac{11 130}{130}

cos (θ) = \frac{11 130}{130}

Apply trig inverse properties

cos (θ) = \frac{11 130}{130}

General solutions for

cos (θ) = \frac{11 130}{130}

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

θ = arccos (\frac{11 130}{130}) + 2 πn, θ = 2 π - arccos (\frac{11 130}{130}) + 2 πn

θ = arccos (\frac{11 130}{130}) + 2 πn, θ = 2 π - arccos (\frac{11 130}{130}) + 2 πn

Show solutions in decimal form

θ = 0.26625 \dots + 2 πn, θ = 2 π - 0.26625 \dots + 2 πn

2 sin^{2} (u) = 1 - sin (u)

2 cos^{2} (x) = 1 - sin (x)

sin (t) = - \frac{3}{2}

2 sin (2 θ) - 3 sin (θ) = 0

cos^{2} (x) + cos^{2} (\frac{x}{2}) - \frac{1}{2} = 0

What is the general solution for cos(θ)=(11)/(sqrt(130)) ?
The general solution for cos(θ)=(11)/(sqrt(130)) is θ=0.26625…+2pin,θ=2pi-0.26625…+2pin