What is the general solution for cos(θ)= 20/25 ?

The general solution for cos(θ)= 20/25 is θ=0.64350…+2pin,θ=2pi-0.64350…+2pin

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cos(θ)= 20/25

cos (θ) = \frac{20}{25}

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

Solution steps

cos (θ) = \frac{20}{25}

Cancel the common factor:

5

cos (θ) = \frac{4}{5}

Apply trig inverse properties

θ = arccos (\frac{4}{5}) + 2 πn, θ = 2 π - arccos (\frac{4}{5}) + 2 πn

Show solutions in decimal form

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

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

4 sin (2 θ) = 0

cos (4 θ) = \frac{1}{2}

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

2 cos^{2} (θ) + 2 cos (θ) - 1 = 0

What is the general solution for cos(θ)= 20/25 ?
The general solution for cos(θ)= 20/25 is θ=0.64350…+2pin,θ=2pi-0.64350…+2pin