# How to scale the sinusoid on the range $[0, 4\pi]$ to the sinusoid on the range $[1/10, 2/10]$?

How to scale the sinusoid on the range $$[0, 4pi]$$ to the sinusoid on the range $$[\frac{1}{10}, \frac{2}{10}]$$?

I've had a couple of approaches, but I don't know how to do it. I tried use translation and it's simple, but difficult to me is linear scale

I'd like to use a python to plot: import numpy as np
x = np.linspace(0,4*np.pi)

y = np.sin(x)

import matplotlib.pyplot as plt
plt.plot(x, y)


Edit: My bug:

import numpy as np
x = (np.linspace(0,4*np.pi))

y = np.sin(x)* (1/(40*np.pi)) + 1/10
print(y)
import matplotlib.pyplot as plt
plt.plot(x, np.sin(x))


Notice that you're trying to squeeze two wave forms into a length of $$\frac{1}{10}$$ which means that the period of your function should be $$T = \frac{1}{20}$$. Given the formula
$$\omega \;\; =\;\; \frac{2\pi}{T} \;\; =\;\; 40\pi$$
and the fact that you want to shift it to the right $$\frac{1}{10}$$ then your function is
$$f(x) \;\; =\;\; \sin\left [40\pi \left ( x - \frac{1}{10} \right )\right ].$$
• Where x belongs to? $x \in [0,4pi]$? Apr 29, 2020 at 21:47
• It's wrong, for example if $x=1/10$ then $f(x) \neq 0$ Apr 29, 2020 at 21:48