How to Linearize an R vs θ graph (distance vs angle)

[Bianca526]

TL;DR Summary

I wanted to ask if there was any way I could linearize this graph? Its a displacement vs angle graph and Im having difficulty trying to figure out how to linearize it.

 

[Vanadium 50]

In pieces maybe?

 

[Bianca526]

If I may ask, how would I do that?

 

[nasu]

Why do you want to linearize it? And more importantly, what makes you think that it can be linearized?

 

[DaveE]

I'll assume that you mean you want to approximate it's value with a linear function?

In a global sense, this certainly isn't a linear function. So, over a large domain, you can't linearize it with any reasonable accuracy.

However, any well behaved function can be approximated by a line in a small enough domain. It's as simple as calculating the slope of the curve at the point you want to approximate around, then, combined with the value at that point you can solve for the linear approximation; y = m⋅x + b. Do you know about derivatives? That is the key, that is what m is.

Then the real problem comes when you want to know how accurate your approximation is over some domain around the point. For that you'll want to learn about Taylor Series.

Alternatively, you can define your domain as a certain number of points and use linear regression to calculate the best linear fit.

In either case Wikipedia is a good place to get more information.

 

[Vanadium 50]

If I may ask, how would I do that?

One linear approximation from (e.g.) 0 to 10. Another from 10-20. Another from 20-30. And so on.

 

[tech99]

Summary:: I wanted to ask if there was any way I could linearize this graph? Its a displacement vs angle graph and I am having difficulty trying to figure out how to linearize it.

View attachment 274151

It tends to follow Y = sin (2xangle) apart from the first few points which seem to be outliers from a straight line.