# Determining the Equation of a Sine and Cosine Graph that speeds up

• I
• FGD
In summary, there is no easy way to speed up the left side of the function without affecting the right side.
FGD
TL;DR Summary
What is the equation I would need to fit my function to the graph?
My function needs to speed up towards the left. How do I do this?

Green is the graph.
Red is my function that needs to match the graph.
A = Amplitude = -0.13
H = Phase Shift = 0.1625
V = Vertical Shift = 0.05
P = period = 0.4
B = 2π / P
Y = A (Cos(B (X-H) ) + V

Using that function, there is no way to "speed up" the left side without changing the right side. The parameter B controls the "speed" evenly across the entire thing.

Is there another function that would work?

My immediate answer is to treat the two sides separately, using the same function but changing B. Is that ok? For other ideas, you should specify any additional requirements that you have.

Good suggestion. You just gave me another thought. Would there be some way to alter B based on X?
The additional requirements are that this data set will be compared against multiple with the same function. My worst fit is this data set. (Again faster frequency on the left. Red is my function)

FGD said:
Good suggestion. You just gave me another thought. Would there be some way to alter B based on X?
The additional requirements are that this data set will be compared against multiple with the same function. My worst fit is this data set. (Again faster frequency on the left. Red is my function)View attachment 264304
I don't know a good way to change B smoothly based on x, because that would change the right side. What I had in mind was something where you leave B with its current value when x > H and give it a larger value when x < H.

Here is the full data set. The order is Red, Green, Pink, Yellow, Blue, Purple. If I can get this function to work then I hopefully can get each data set to morph into the next over time.

Yeah something very similar to the bicubic example in that link.

FGD said:
Yeah something very similar to the bicubic example in that link.
If you can use something like MATLAB, it has some fairly sophisticated curve-fitting tools. See https://www.mathworks.com/help/curvefit/multivariate-and-rational-splines.html

If MATLAB is not available to you, you might look at the free statistical package, R. The first answer here has the R code for a multivariate interpolation using a referenced package. I have no experience with it.

## 1. How do I determine the equation of a sine and cosine graph that speeds up?

To determine the equation of a sine or cosine graph that speeds up, you will need to know the amplitude, period, and phase shift of the graph. These values can be determined by analyzing the graph or by using a mathematical formula. Once you have these values, you can use the general equations for sine and cosine graphs to write the equation for the speeding up graph.

## 2. What is the difference between a sine and cosine graph that speeds up?

The main difference between a sine and cosine graph that speeds up is the phase shift. In a sine graph, the phase shift is 0 degrees, while in a cosine graph, the phase shift is 90 degrees. This means that the starting point for the graph is different, resulting in a different shape and pattern.

## 3. How can I determine the amplitude of a speeding up sine or cosine graph?

The amplitude of a speeding up sine or cosine graph can be determined by finding the difference between the maximum and minimum values on the graph. This value represents the vertical distance between the center line and the peak or trough of the graph.

## 4. Can I use a calculator to determine the equation of a speeding up sine or cosine graph?

Yes, you can use a scientific or graphing calculator to determine the equation of a speeding up sine or cosine graph. These calculators have built-in functions that can help you find the amplitude, period, and phase shift of the graph, making it easier to write the equation.

## 5. How do I know if my equation for a speeding up sine or cosine graph is correct?

To ensure that your equation for a speeding up sine or cosine graph is correct, you can use a graphing calculator to plot the equation and compare it to the original graph. If the two graphs match, then your equation is correct. You can also check your equation by plugging in different values for x and ensuring that the resulting y-values match the graph.

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