Question

Построить график функции Y=3cos(2x+p\3)

Answer 1

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Answer 2

Graph of the Function Y = 3cos(2x + p/3)

To graph the function Y = 3cos(2x + p/3), we can start by understanding the properties of the cosine function and how they affect the graph.

The general form of the cosine function is Y = A*cos(Bx + C), where A, B, and C are constants that determine the amplitude, period, and phase shift of the graph, respectively.

In our case, the function is Y = 3cos(2x + p/3). Let's break down the components:

- Amplitude (A): The amplitude of the cosine function determines the maximum and minimum values of the graph. In this case, the amplitude is 3, which means the graph will oscillate between 3 and -3.

- Period (T): The period of the cosine function determines the length of one complete cycle. The period is given by T = 2p/B, where B is the coefficient of x in the function. In this case, B = 2, so the period is T = 2p/2 = p.

- Phase Shift (C): The phase shift of the cosine function determines the horizontal shift of the graph. In this case, C = p/3, which means the graph will be shifted to the left by p/3 units.

Now that we have the properties of the function, we can proceed to graphing it.

To create the graph, we can plot several points and connect them to form a smooth curve. Let's choose some values for x and calculate the corresponding y values using the function Y = 3cos(2x + p/3):

| x | Y = 3cos(2x + p/3) | |----|-------------------| | -2 | 3cos(-4p/3) | | -1 | 3cos(-2p/3) | | 0 | 3cos(p/3) | | 1 | 3cos(4p/3) | | 2 | 3cos(2p/3) |

Now, let's calculate the y values:

| x | Y = 3cos(2x + p/3) | |----|-------------------| | -2 | 3cos(-4p/3) | | -1 | 3cos(-2p/3) | | 0 | 3cos(p/3) | | 1 | 3cos(4p/3) | | 2 | 3cos(2p/3) | | -2 | 3cos(-4p/3) |

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

Plotting the points:
(-2, 3cos(-4p/3))
(-1, 3cos(-2p/3))
(0, 3cos(p/3))
(1, 3cos(4p/3))
(2, 3cos(2p/3))

Connecting these points will give us the graph of the function Y = 3cos(2x + p/3).

Note: The graph will repeat itself every p units, so you can continue plotting points beyond the ones listed above to see the complete graph.

I hope this helps! Let me know if you have any further questions.