What is the general solution for cos(θ)= 1/(sqrt(3)) ?

The general solution for cos(θ)= 1/(sqrt(3)) is θ=0.95531…+2pin,θ=2pi-0.95531…+2pin

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cos(θ)= 1/(sqrt(3))

cos (θ) = \frac{1}{3}

θ = 0.95531 \dots + 2 πn, θ = 2 π - 0.95531 \dots + 2 πn

Radians

θ = 0.95531 \dots + 6.28318 \dots n, θ = 5.32786 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{1}{3}

Simplify

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

cos (θ) = \frac{3}{3}

Apply trig inverse properties

cos (θ) = \frac{3}{3}

General solutions for

cos (θ) = \frac{3}{3}

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

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

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

Show solutions in decimal form

θ = 0.95531 \dots + 2 πn, θ = 2 π - 0.95531 \dots + 2 πn

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

4 csc (θ) - 5 = 3

csc (5 x) = - 1, 0 \leq x \leq 2 π

- 4 \cdot cos^{2} (x) + 3 = 0

8 sin (θ) + 1 = 6 sin (θ)

What is the general solution for cos(θ)= 1/(sqrt(3)) ?
The general solution for cos(θ)= 1/(sqrt(3)) is θ=0.95531…+2pin,θ=2pi-0.95531…+2pin