What is the general solution for cos(α)=(sqrt(5))/3 ?

The general solution for cos(α)=(sqrt(5))/3 is α=0.72972…+2pin,α=2pi-0.72972…+2pin

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cos(α)=(sqrt(5))/3

cos (α) = \frac{5}{3}

α = 0.72972 \dots + 2 πn, α = 2 π - 0.72972 \dots + 2 πn

Degrees

α = 41.81031 \dots^{\circ} + 36 0^{\circ} n, α = 318.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (α) = \frac{5}{3}

Apply trig inverse properties

cos (α) = \frac{5}{3}

General solutions for

cos (α) = \frac{5}{3}

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

α = arccos (\frac{5}{3}) + 2 πn, α = 2 π - arccos (\frac{5}{3}) + 2 πn

α = arccos (\frac{5}{3}) + 2 πn, α = 2 π - arccos (\frac{5}{3}) + 2 πn

Show solutions in decimal form

α = 0.72972 \dots + 2 πn, α = 2 π - 0.72972 \dots + 2 πn

2 - 3 sin (x) - cos (2 x) = 0

cos (2 θ) = \frac{1}{4}

sec (θ) = \frac{25}{7}

(3 + sin (x))^{2} = 13 - cos^{2} (x)

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π

What is the general solution for cos(α)=(sqrt(5))/3 ?
The general solution for cos(α)=(sqrt(5))/3 is α=0.72972…+2pin,α=2pi-0.72972…+2pin