Sine Curve Simultaneous equation help

Hello everyone, this is my first post, be kind =).

I have three sin curves, for 'biorhytms' (those lame scenarios they gives us for math assignments) each with a different period the equations are as follows;

y=sin(2pi/33*x)
y=sin(2pi/23*x)
y=sin(2pi/28*x)

where x is the number of days after birth. What I'm trying to find is the day in which all three curves equal zero, after x=0 of coruse. I get down to a whole number integar of the period on two for each one. And realised it must be a common multiple of all three, but how best do you show this? Thank you! Any help is much appreciated!

Quote:

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Originally Posted by zooloo45

Hello everyone, this is my first post, be kind =).

I have three sin curves, for 'biorhytms' (those lame scenarios they gives us for math assignments) each with a different period the equations are as follows;

y=sin(2pi/33*x)
y=sin(2pi/23*x)
y=sin(2pi/28*x)

where x is the number of days after birth. What I'm trying to find is the day in which all three curves equal zero, after x=0 of coruse. I get down to a whole number integar of the period on two for each one. And realised it must be a common multiple of all three, but how best do you show this? Thank you! Any help is much appreciated!

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when k is an integer. In your case this would be when

2x/33, 2x/23 and 2x/28 are all equal to an integer and therefore the LCD needs to be found.

I find their LCD to be 21252 and so x = 10626