## Python Taylor series sin function graph

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I'm trying to draw a Taylor series sin(x) graph using python with Jupyter notebook. I created a short function. The graph will appear correctly until `y2`

, but it will fail at `y3`

. It is difficult to draw a graph with a value of `x = 2.7`

in `y3`

. I don't know how to fix `y3`

.

This is my code:

import numpy as np import matplotlib.pyplot as plt import numpy as np def f(x) : result = x - x**3/6 + x**5/120 return result x = np.linspace(0.0, 7.0, 100) y = np.sin(x) y2 = x - x**3/6 + x**5/120 y3 = f(2.7) plt.title("taylor sin graph") plt.xlim(0, 7+0.2) plt.ylim(-5, 5+1) plt.plot(x, y, label='sin(x)') plt.plot(x, y2, label='x=0') plt.plot(x, y3, label='x=2.7') plt.legend() plt.show()

I want to add `y3`

here:

After your comment, it got clarified that you do not need a single point but a horizontal line. In that case you can simply input an x-mesh which has the same value `2.7`

.

To do so, you first define an array containing values `2.7`

by using `np.ones(100) * 2.7`

and then just pass it to the function.

y3 = f(2.7*np.ones(100)) plt.plot(x, y3, label='x=2.7')

For plotting a single point at `x=2.7`

, there are two ways (among possible others).

**First option** is to just specify the two x-y numbers and plot using a marker as

plt.plot(2.7, y3, 'bo', label='x=2.7')

**Second option** is to use `plt.scatter`

. `s=60`

is just to have a big marker.

plt.scatter(2.7, y3, s=60, label='x=2.7')

**Taylor Series in Python,** Then we will refactor the Taylor Series into functions and compare the output of Below is a chart that shows each term of the Taylor Series in a row. Next, let's calculate the value of the cosine function using a Taylor Series. Both math.sin and my Taylor Polynomial function take radians so we set a variable using math.radians. (Thank you Python People for having the sense to provide this function; the implementors of some languages don't bother.) The sine is then calculated using math.sin, the y cooridinate is calculated and the colour index reset to 0. Next we plot the sine with a small circle.

import numpy as np import matplotlib.pyplot as plt import numpy as np def f(x) : result = x - x**3/6 + x**5/120 return result x = np.linspace(0.0, 7.0, 100) y = np.sin(x) y2 = x - x**3/6 + x**5/120 y3 = f(2.7) plt.title("taylor sin graph") plt.xlim(0, 7+0.2) plt.ylim(-5, 5+1) plt.plot(x, y, label='sin(x)') plt.plot(x, y2, label='x=0') plt.plot(2.7, y3, label='x=2.7', marker=11) plt.legend() plt.show()

You have to add point - not an array in x-axis and scalar on y-axis.

**Plotting the Taylor Series for sine,** Before I get to that, if you don't know, the Taylor Series for sin(x), To make the plot, we define a "factory" function that returns functions for the One line for Python's cos() function and one line for our func_cos() function with three terms in the Taylor series approximation. We'll calculate the cosine using both functions for angles between $-2\pi$ radians and $2\pi$ radians.

I think

plt.plot([2.7], [y3], '-o', label='x=2.7')

would work. You can't plot(x,y3) when x is a linspace and y3 is just one number.

Also, Taylor approximation of sin function works only in the interval (-pi, pi).

**Plotting Taylor Series Polynomials in Python,** sin function; this can be taken as a definitive set of values. The other colours are sines calculated using Taylor Polynomials to various degrees, ie Before I get to that, if you don't know, the Taylor Series for sin(x), cos(x) and e x can be used to derive Euler's famous formula, which we touched on briefly a while back (here and here). The project: there is a terrific graphic in the wikipedia article showing what a good approximation one can get with only a few terms from the series.

**Taylor series with Python and Sympy,** Here is the output of the plot function for the function sin(x) approximating up to the Taylor expansion at n=7 -x**7/5040 + x**5/120 - x**3/6 + x. A Taylor series is a representation of a function using an infinite sum. Computers often make approximations of the values of a trigonometric, exponential or other transcendental function by summing a finite number of the terms of its Taylor series, and you can recreate this process in Python.

**Taylor Series Expansion with Python · Data Science Fabric,** Taylor and Maclaurin Series Expansion for functions with Python. Symbol from sympy.functions import sin, cos, exp from sympy.plotting In Python, math module contains a number of mathematical operations, which can be performed with ease using the module. math.sin () function returns the sine of value passed as argument. The value passed in this function should be in radians. Syntax: math.sin (x) Parameter: x : value to be passed to sin () Returns: Returns the sine of value passed as argument.

**Univariate Taylor Series Expansions,** As an easy example we want to compute the Taylor series expansion of import numpy; from numpy import sin,cos from algopy import UTPM def f(x): return the correct Taylor series expansion we plot the original function and the Taylor Taylor Series Expansion with Python In this blog, I want to review famous Taylor Series Expansion and its special case Maclaurin Series Expansion. According to wikipedia , the aim of Taylor Series Expansion (TSE) is to represent a function as an infinite sum of terms that are derived from the values of that function's derivatives, which in turn

##### Comments

- Hi and welcome to stackoverflow. What is y3 supposed to be? In your code, it's a single value, the function calculated in 2.7. Now, if you plot a single point, you get a single dot on the plot, which will be nearly invisible.
`f`

is returning a single value. Doing`f(2.7)`

doesn't make much sense.- It is unclear what you want to happen with
`y3 = f(2.7)`

. This will only return a single value. If you use`y3 = f(x)`

, then you will get the identical plot that you get for`y2`

. - @ChrisMueller: May be the OP wants just to highlight the value at one point
- I don't think you need to make your option 1 values lists?
`plt.plot(2.7, y3, 'bo', label='x=2.7')`

works - @Bazingaa thankyou for help! and i have another question. How do I make a graph of x=2.7 in one line that doesn't break like an x=0 or sinx graph? How should I fix the function?
- @uenbh: What do you mean? Do you mean horizontal line?
- @DavidG: Thanks, I edited. I still kept the list thing as one possibility but moved it to additional option
- @Bazingaa yes. I want to compare the Taylor approximation polynomial graph. I want to make x=2.7 graph a long line graph format rather than a dot. I want it to be expressed in the same format as sin or x = 0 graph.
- i have another question. How do I make a graph of x=2.7 in one line that doesn't break like an x=0 or sinx graph? How should I fix the function?