Math Problem Statement

Постройте графики функций!

а) y = 2cosx

б) y = sin 2x

в) y = 2sinx + 3

Solution

numpy as np import matplotlib.pyplot as plt

Define the x values for plotting

x = np.linspace(-2 * np.pi, 2 * np.pi, 400)

Define the functions

y1 = 2 * np.cos(x) y2 = np.sin(2 * x) y3 = 2 * np.sin(x) + 3

Create the plots

plt.figure(figsize=(12, 8))

Plot for y = 2cos(x)

plt.subplot(3, 1, 1) plt.plot(x, y1, label=r'$y = 2 \cos(x)$') plt.title(r'$y = 2 \cos(x)$') plt.grid(True) plt.axhline(0, color='black',linewidth=1) plt.axvline(0, color='black',linewidth=1) plt.legend(loc='upper right')

Plot for y = sin(2x)

plt.subplot(3, 1, 2) plt.plot(x, y2, label=r'$y = \sin(2x)$') plt.title(r'$y = \sin(2x)$') plt.grid(True) plt.axhline(0, color='black',linewidth=1) plt.axvline(0, color='black',linewidth=1) plt.legend(loc='upper right')

Plot for y = 2sin(x) + 3

plt.subplot(3, 1, 3) plt.plot(x, y3, label=r'$y = 2 \sin(x) + 3$') plt.title(r'$y = 2 \sin(x) + 3$') plt.grid(True) plt.axhline(0, color='black',linewidth=1) plt.axvline(0, color='black',linewidth=1) plt.legend(loc='upper right')

Adjust layout and show the plot

plt.tight_layout() plt.show()Вот графики для заданных функций:

  1. y=2cos(x)y = 2 \cos(x) — график косин

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Graphing Trigonometric Functions

Formulas

y = 2cos(x)
y = sin(2x)
y = 2sin(x) + 3

Theorems

Basic Trigonometric Identities
Graphing of Trigonometric Functions

Suitable Grade Level

Grades 9-12