What is the general solution for cos(θ)=(1/4) ?

The general solution for cos(θ)=(1/4) is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin

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cos(θ)=(1/4)

cos (θ) = (\frac{1}{4})

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

Degrees

θ = 75.52248 \dots^{\circ} + 36 0^{\circ} n, θ = 284.47751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = (\frac{1}{4})

Apply trig inverse properties

cos (θ) = \frac{1}{4}

General solutions for

cos (θ) = \frac{1}{4}

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

θ = arccos (\frac{1}{4}) + 2 πn, θ = 2 π - arccos (\frac{1}{4}) + 2 πn

θ = arccos (\frac{1}{4}) + 2 πn, θ = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn

- cos^{2} (x) = sin (x) + 1

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}

6 sin (\frac{x}{2}) + 6 cos (x) = 0

cos (x) = 0.925

(sin (x) + 1) (2 sin^{2} (x) - 3 sin (x) - 2) = 0

What is the general solution for cos(θ)=(1/4) ?
The general solution for cos(θ)=(1/4) is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin