What is the general solution for cos(θ)= 3/(sqrt(34)) ?

The general solution for cos(θ)= 3/(sqrt(34)) is θ=1.03037…+2pin,θ=2pi-1.03037…+2pin

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cos(θ)= 3/(sqrt(34))

cos (θ) = \frac{3}{34}

θ = 1.03037 \dots + 2 πn, θ = 2 π - 1.03037 \dots + 2 πn

Radians

θ = 1.03037 \dots + 6.28318 \dots n, θ = 5.25280 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{3}{34}

Simplify

\frac{3}{34} : \frac{3 34}{34}

\frac{3}{34}

Multiply by the conjugate

\frac{34}{34}

= \frac{3 34}{34 34}

3434 = 34

3434

Apply radical rule:

a a = a

3434 = 34

= 34

= \frac{3 34}{34}

cos (θ) = \frac{3 34}{34}

Apply trig inverse properties

cos (θ) = \frac{3 34}{34}

General solutions for

cos (θ) = \frac{3 34}{34}

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

θ = arccos (\frac{3 34}{34}) + 2 πn, θ = 2 π - arccos (\frac{3 34}{34}) + 2 πn

θ = arccos (\frac{3 34}{34}) + 2 πn, θ = 2 π - arccos (\frac{3 34}{34}) + 2 πn

Show solutions in decimal form

θ = 1.03037 \dots + 2 πn, θ = 2 π - 1.03037 \dots + 2 πn

tan (θ) + cot (θ) = \frac{4}{3}

sec (x) + 4 cos (x) = 5

- 3 sec (x) = 2

3 cos (x) csc (x) = 23 cos (x)

cos (2 x) = \frac{9}{41}

What is the general solution for cos(θ)= 3/(sqrt(34)) ?
The general solution for cos(θ)= 3/(sqrt(34)) is θ=1.03037…+2pin,θ=2pi-1.03037…+2pin