What is the general solution for 1/3 =cos((pix)/(12)) ?

The general solution for 1/3 =cos((pix)/(12)) is x=(12*1.23095…)/pi+24n,x=24-(12*1.23095…)/pi+24n

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1/3 =cos((pix)/(12))

\frac{1}{3} = cos (\frac{π x}{12})

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

Solution steps

\frac{1}{3} = cos (\frac{π x}{12})

Switch sides

cos (\frac{π x}{12}) = \frac{1}{3}

Apply trig inverse properties

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn, \frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

Solve

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn : x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

Solve

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn : x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n, x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

Show solutions in decimal form

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

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What is the general solution for 1/3 =cos((pix)/(12)) ?
The general solution for 1/3 =cos((pix)/(12)) is x=(12*1.23095…)/pi+24n,x=24-(12*1.23095…)/pi+24n