What is the general solution for cos(1/(3x))= 1/3 ?

The general solution for cos(1/(3x))= 1/3 is x= 1/(3(1.23095…+2pin)),x= 1/(3(2pi-1.23095…+2pin))

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cos(1/(3x))= 1/3

cos (\frac{1}{3 x}) = \frac{1}{3}

x = \frac{1}{3 ( 1.23095 \dots + 2 πn )}, x = \frac{1}{3 ( 2 π - 1.23095 \dots + 2 πn )}

Solution steps

cos (\frac{1}{3 x}) = \frac{1}{3}

Apply trig inverse properties

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn, \frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

Solve

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn : x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

Solve

\frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn : x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}, x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}

Show solutions in decimal form

x = \frac{1}{3 ( 1.23095 \dots + 2 πn )}, x = \frac{1}{3 ( 2 π - 1.23095 \dots + 2 πn )}

arctan (1 + x) + arctan (1 - x) = arctan (\frac{1}{2})

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sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) = 0

What is the general solution for cos(1/(3x))= 1/3 ?
The general solution for cos(1/(3x))= 1/3 is x= 1/(3(1.23095…+2pin)),x= 1/(3(2pi-1.23095…+2pin))