What is the general solution for cos(θ)= 1/(sqrt(21)) ?

The general solution for cos(θ)= 1/(sqrt(21)) is θ=1.35080…+2pin,θ=2pi-1.35080…+2pin

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cos(θ)= 1/(sqrt(21))

cos (θ) = \frac{1}{21}

θ = 1.35080 \dots + 2 πn, θ = 2 π - 1.35080 \dots + 2 πn

Radians

θ = 1.35080 \dots + 6.28318 \dots n, θ = 4.93237 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{1}{21}

Simplify

\frac{1}{21} : \frac{21}{21}

\frac{1}{21}

Multiply by the conjugate

\frac{21}{21}

= \frac{1 \cdot 21}{21 21}

1 \cdot 21 = 21

2121 = 21

2121

Apply radical rule:

a a = a

2121 = 21

= 21

= \frac{21}{21}

cos (θ) = \frac{21}{21}

Apply trig inverse properties

cos (θ) = \frac{21}{21}

General solutions for

cos (θ) = \frac{21}{21}

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

θ = arccos (\frac{21}{21}) + 2 πn, θ = 2 π - arccos (\frac{21}{21}) + 2 πn

θ = arccos (\frac{21}{21}) + 2 πn, θ = 2 π - arccos (\frac{21}{21}) + 2 πn

Show solutions in decimal form

θ = 1.35080 \dots + 2 πn, θ = 2 π - 1.35080 \dots + 2 πn

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

3 sin (x) = sin (3 x)

tan (x) + 3 = 1 + 3 cot (x)

tan (u) - cot (u) = 2

sin (x) sin (x) = 0

What is the general solution for cos(θ)= 1/(sqrt(21)) ?
The general solution for cos(θ)= 1/(sqrt(21)) is θ=1.35080…+2pin,θ=2pi-1.35080…+2pin