Math Help - Sine Curve Simultaneous equation help

1. 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!

2. 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!
$sin(k\pi) = 0$ 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