What is the general solution for cos(θ)=(2sqrt(5))/(sqrt(58)) ?

The general solution for cos(θ)=(2sqrt(5))/(sqrt(58)) is θ=0.94317…+2pin,θ=2pi-0.94317…+2pin

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cos(θ)=(2sqrt(5))/(sqrt(58))

cos (θ) = \frac{2 5}{58}

θ = 0.94317 \dots + 2 πn, θ = 2 π - 0.94317 \dots + 2 πn

Radians

θ = 0.94317 \dots + 6.28318 \dots n, θ = 5.34000 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{2 5}{58}

Simplify

\frac{2 5}{58} : \frac{10}{29}

\frac{2 5}{58}

Factor

58 : 229

Factor

58 = 2 \cdot 29

= 2 \cdot 29

Apply radical rule:

= 229

= \frac{2 5}{2 29}

Cancel

\frac{2 5}{2 29} : \frac{2 5}{29}

\frac{2 5}{2 29}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2 5}{2 ^{\frac{1}{2}} 29}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{5 \cdot 2 ^{- \frac{1}{2} + 1}}{29}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2 ^{\frac{1}{2}} 5}{29}

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{2 5}{29}

= \frac{2 5}{29}

Simplify

25 : 10

25

Apply radical rule:

a b = a \cdot b

25 = 2 \cdot 5

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

= \frac{10}{29}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{10}{29}

Apply trig inverse properties

cos (θ) = \frac{10}{29}

General solutions for

cos (θ) = \frac{10}{29}

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

θ = arccos (\frac{10}{29}) + 2 πn, θ = 2 π - arccos (\frac{10}{29}) + 2 πn

θ = arccos (\frac{10}{29}) + 2 πn, θ = 2 π - arccos (\frac{10}{29}) + 2 πn

Show solutions in decimal form

θ = 0.94317 \dots + 2 πn, θ = 2 π - 0.94317 \dots + 2 πn

tan (θ) = \frac{m ^{2} - m ^{1}}{1 + m ^{2} \cdot m ^{1}}, m^{2}

0 = - 1 - tan^{2} (θ) + 2 tan (θ)

u, x = tanh (u)

3 + 2 cos (x) = 0

2 cos^{2} (θ) - 7 cos (θ) = - 3

What is the general solution for cos(θ)=(2sqrt(5))/(sqrt(58)) ?
The general solution for cos(θ)=(2sqrt(5))/(sqrt(58)) is θ=0.94317…+2pin,θ=2pi-0.94317…+2pin