What function or operation am I looking for?

[minio]

First, I am sorry for very unspecific topic, but I really have no clue what I am looking for. I need some way how in mathematical terms describe things like following:
I have line segment of length $l$ and I have sine function with period length $\lambda$ originating at one end of line segment. If $l$=$\lambda$ I can easily count that there will be three points on the segment where sine value will be 0. But If $\lambda$ is slightly shorter there still will be three such points until $l=\frac{3}{2}\lambda$. Then there will be four of them. How can I describe number of such points as $f(l,\lambda)$?
What should I look for/study? Frankly I wouldn't be surprised if it is something really basic, because I tend to miss basic things :/ Thank you in advance

 

[dodo]

So, you want to know how many zeroes are in a sine wave $l/\lambda$ periods long. Which should be $\lfloor 2l/\lambda \rfloor+1$ zeroes in total, where the brackets represent the floor function.

 

[minio]

Thank you. I never heard of floor function before. Now it is clear, that in general I was looking for floor/ceiling functions.

 

[dodo]

You're welcome!

If the ratio $2l/\lambda$ is positive (as it will presumably be in your case), then $\lfloor 2l/\lambda \rfloor$ is simply the integer part of that ratio. For example, if $2l/\lambda$ was 17.936, then $\lfloor 2l/\lambda \rfloor$ would be just 17.

 

[CellCoree]

Based on the information provided, it seems like you are looking for a mathematical function or operation that can describe the relationship between the length of a line segment and the number of points on that segment where the sine value is 0. This could potentially be described as a function of the form f(l,\lambda) where l represents the length of the line segment and \lambda represents the period length of the sine function originating at one end of the segment.

To find this function, you may need to study trigonometry and specifically the properties and behaviors of sine functions. This will help you understand how the period length \lambda affects the number of points where the sine value is 0 on a given line segment. Additionally, studying basic algebra and functions may also be helpful in finding a way to describe this relationship mathematically.

Overall, it is important to have a strong understanding of the concepts and properties involved in order to accurately describe the relationship between these variables. I recommend consulting with a math teacher or tutor for further guidance and assistance in finding the appropriate function or operation.