What is the general solution for cos(θ)= 5/20 ?

The general solution for cos(θ)= 5/20 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin

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cos(θ)= 5/20

cos (θ) = \frac{5}{20}

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{5}{20}

Cancel the common factor:

5

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

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

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

sin^{4} (x) - 2 sin^{2} (x) + 1 = 0

- 2 sin (x) = 3

(\frac{2}{2}) (cos (θ) + sin (θ)) = 1

What is the general solution for cos(θ)= 5/20 ?
The general solution for cos(θ)= 5/20 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin