Sine function whose period is $6$ is

s i n \frac{2 π x}{3}

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s i n \frac{π x}{3}

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s i n \frac{π x}{6}

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s i n \frac{3 π x}{2}

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Solution

The correct option is B $s i n \frac{π x}{3}$
Let $f (x) = sin (k x)$
Period of $f (x) = \frac{2 π}{| k |} = 6$
$∴ | k | = \frac{π}{3}$
$∴ f (x) = s i n (\frac{π x}{3})$

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