What is the general solution for cos(α)= 2/3 ?

The general solution for cos(α)= 2/3 is α=0.84106…+2pin,α=2pi-0.84106…+2pin

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cos(α)= 2/3

cos (α) = \frac{2}{3}

α = 0.84106 \dots + 2 πn, α = 2 π - 0.84106 \dots + 2 πn

Solution steps

cos (α) = \frac{2}{3}

Apply trig inverse properties

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

Show solutions in decimal form

α = 0.84106 \dots + 2 πn, α = 2 π - 0.84106 \dots + 2 πn

sec (- 2 x) = - 2

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

sin (x) sec (x) = 2 sin (x), 0 \leq x \leq 2 π

3 cos^{2} (y) - 1 = cos (y) + cos^{2} (y), π \leq y \leq 2 π

sec^{2} (x) + tan (x) = 1, 0 \leq x \leq 2 π

What is the general solution for cos(α)= 2/3 ?
The general solution for cos(α)= 2/3 is α=0.84106…+2pin,α=2pi-0.84106…+2pin