What is the general solution for cos(θ)= 1/5 ?

The general solution for cos(θ)= 1/5 is θ=1.36943…+2pin,θ=2pi-1.36943…+2pin

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cos(θ)= 1/5

cos (θ) = \frac{1}{5}

θ = 1.36943 \dots + 2 πn, θ = 2 π - 1.36943 \dots + 2 πn

Degrees

θ = 78.46304 \dots^{\circ} + 36 0^{\circ} n, θ = 281.53695 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{1}{5}

Apply trig inverse properties

cos (θ) = \frac{1}{5}

General solutions for

cos (θ) = \frac{1}{5}

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

θ = arccos (\frac{1}{5}) + 2 πn, θ = 2 π - arccos (\frac{1}{5}) + 2 πn

θ = arccos (\frac{1}{5}) + 2 πn, θ = 2 π - arccos (\frac{1}{5}) + 2 πn

Show solutions in decimal form

θ = 1.36943 \dots + 2 πn, θ = 2 π - 1.36943 \dots + 2 πn

sin (\frac{x}{2}) - cos (x) = 0

3 sin (x) = 3 - 3 cos (x)

0 = 1 - 2 cos (x)

- 5 sin^{2} (θ) + 17 cos (θ) + 9 = 4 cos (θ) - 2

(cos (3 θ)) (cos (θ)) + 1 = (sin (3 θ)) (sin (θ))

What is the general solution for cos(θ)= 1/5 ?
The general solution for cos(θ)= 1/5 is θ=1.36943…+2pin,θ=2pi-1.36943…+2pin