Question

Построить график функции y=3sin(x-П/2)+5 и y=2sin(x+П/4)-3 помогите

Answer 1

Графики в приложении.  Где +5, а где -3 - понятно без пояснений.

Answer 2

Graphing the Functions

To graph the functions y=3sin(x-π/2)+5 and y=2sin(x+π/4)-3, we can use the standard form of the sine function, which is y = A sin(Bx - C) + D. Here, A represents the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

For the function y=3sin(x-π/2)+5: - Amplitude (A) = 3 - Period = 2π/B - Phase Shift = C - Vertical Shift = D

For the function y=2sin(x+π/4)-3: - Amplitude (A) = 2 - Period = 2π/B - Phase Shift = -C - Vertical Shift = D

Let's plot these functions to visualize their behavior.

Graphical Representation

```python import numpy as np import matplotlib.pyplot as plt

x = np.linspace(-2*np.pi, 2*np.pi, 1000) y1 = 3 * np.sin(x - np.pi/2) + 5 y2 = 2 * np.sin(x + np.pi/4) - 3

plt.figure(figsize=(10, 6)) plt.plot(x, y1, label='y=3sin(x-π/2)+5') plt.plot(x, y2, label='y=2sin(x+π/4)-3') plt.title('Graphs of y=3sin(x-π/2)+5 and y=2sin(x+π/4)-3') plt.xlabel('x') plt.ylabel('y') plt.legend() plt.grid(True) plt.show() ```

The graph will show the behavior of the two functions and how they differ in terms of amplitude, period, phase shift, and vertical shift.

Conclusion

The graph of the functions y=3sin(x-π/2)+5 and y=2sin(x+π/4)-3 illustrates their behavior and how they differ in terms of amplitude, period, phase shift, and vertical shift.