What is the general solution for cos(θ)=(13)/(sqrt(6)*\sqrt{86)} ?

The general solution for cos(θ)=(13)/(sqrt(6)*\sqrt{86)} is θ=0.96149…+2pin,θ=2pi-0.96149…+2pin

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cos(θ)=(13)/(sqrt(6)*\sqrt{86)}

cos (θ) = \frac{13}{6 \cdot 86}

θ = 0.96149 \dots + 2 πn, θ = 2 π - 0.96149 \dots + 2 πn

Radians

θ = 0.96149 \dots + 6.28318 \dots n, θ = 5.32168 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{13}{6 86}

Simplify

\frac{13}{6 86} : \frac{13 129}{258}

\frac{13}{6 86}

Simplify

686 : 2343

686

Factor integer

6 = 2 \cdot 3

= 2 \cdot 3 86

Apply radical rule:

n ab = n a n b

2 \cdot 3 = 23

= 2386

Factor integer

86 = 2 \cdot 43

= 23 2 \cdot 43

Apply radical rule:

n ab = n a n b

2 \cdot 43 = 243

= 23243

Apply radical rule:

a a = a

22 = 2

= 2343

= \frac{13}{2 3 43}

Simplify

3 \cdot 243 : 2129

3 \cdot 243

Apply radical rule:

a b = a \cdot b

343 = 3 \cdot 43

= 2 3 \cdot 43

Multiply the numbers:

3 \cdot 43 = 129

= 2129

= \frac{13}{2 129}

Rationalize

\frac{13}{2 129} : \frac{13 129}{258}

\frac{13}{2 129}

Multiply by the conjugate

\frac{129}{129}

= \frac{13 129}{129 \cdot 2 129}

129 \cdot 2129 = 258

129 \cdot 2129

Apply radical rule:

a a = a

129129 = 129

= 2 \cdot 129

Multiply the numbers:

2 \cdot 129 = 258

= 258

= \frac{13 129}{258}

= \frac{13 129}{258}

cos (θ) = \frac{13 129}{258}

Apply trig inverse properties

cos (θ) = \frac{13 129}{258}

General solutions for

cos (θ) = \frac{13 129}{258}

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

θ = arccos (\frac{13 129}{258}) + 2 πn, θ = 2 π - arccos (\frac{13 129}{258}) + 2 πn

θ = arccos (\frac{13 129}{258}) + 2 πn, θ = 2 π - arccos (\frac{13 129}{258}) + 2 πn

Show solutions in decimal form

θ = 0.96149 \dots + 2 πn, θ = 2 π - 0.96149 \dots + 2 πn

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

tan (x) + 1 = \frac{1}{3} + \frac{1}{3} cot (x)

sin (8 x) = 1

2 cos^{2} (w) - 3 cos (w) - 5 = 0

4 sin (x) = csc (x)

What is the general solution for cos(θ)=(13)/(sqrt(6)*\sqrt{86)} ?
The general solution for cos(θ)=(13)/(sqrt(6)*\sqrt{86)} is θ=0.96149…+2pin,θ=2pi-0.96149…+2pin