What is the general solution for cos(x)= 5/9 ?

The general solution for cos(x)= 5/9 is x=0.98176…+2pin,x=2pi-0.98176…+2pin

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cos(x)= 5/9

cos (x) = \frac{5}{9}

x = 0.98176 \dots + 2 πn, x = 2 π - 0.98176 \dots + 2 πn

Solution steps

cos (x) = \frac{5}{9}

Apply trig inverse properties

x = arccos (\frac{5}{9}) + 2 πn, x = 2 π - arccos (\frac{5}{9}) + 2 πn

Show solutions in decimal form

x = 0.98176 \dots + 2 πn, x = 2 π - 0.98176 \dots + 2 πn

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

4 tan^{2} (θ) = 11 tan (θ) + 3

6 tan^{2} (x) - 2 cos^{2} (x) = cos (2 x)

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

6 tan (θ) + 5 = 0

What is the general solution for cos(x)= 5/9 ?
The general solution for cos(x)= 5/9 is x=0.98176…+2pin,x=2pi-0.98176…+2pin