Question

Постройте график функции y=2-sin(п/4+x)

Answer 1

Y=-sin(x+П/4)
строим косинусоиду

Answer 2

Plot of the Function y = 2 - sin(π/4 + x)

To plot the function y = 2 - sin(π/4 + x), we can start by analyzing the components of the function:

- The constant term 2 shifts the graph vertically upward by 2 units. - The term sin(π/4 + x) represents a sinusoidal function with a phase shift of π/4 units to the left.

To create a graph, we can plot several points and connect them to form a smooth curve. Let's plot the graph for a range of x values and determine the corresponding y values.

| x | y = 2 - sin(π/4 + x) | | --- | ------------------- | | -2π | 2 | | -π | 2 - √2 | | -π/2| 1 | | 0 | 2 | | π/2 | 3 | | π | 2 + √2 | | 2π | 2 |

Now, let's plot these points on a graph:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-2*np.pi, 2*np.pi, 1000)
y = 2 - np.sin(np.pi/4 + x)

plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = 2 - sin(π/4 + x)')
plt.grid(True)
plt.show()

The resulting graph will show a sinusoidal curve with a vertical shift of 2 units. The curve will oscillate between the values 2 - √2 and 2 + √2.

Graph of y = 2 - sin(π/4 + x)


Please note that the graph is an approximation and may not be perfectly smooth due to the limited number of plotted points.