Question

Как построить график функции y=2sin(2x+п/3)-2 и 1/2cos (1/2x-п/2)+1

Answer 1

$y=2\sin(2x+ \frac{\pi}{3})-2=2\sin(2(x+ \frac{\pi}{6}))-2, \\ 1) y=\sin x, \\ 2) y=\sin2x, \\ 3) y=2\sin2x, \\ 4) Ox\uparrow2, Oy\rightarrow\frac{\pi}{6}.$

$y= \frac{1}{2} \cos( \frac{1}{2} x- \frac{\pi}{2})+1=\frac{1}{2} \cos\frac{1}{2}(x- \pi)+1, \\ 1) y=\cos x, \\ 2) y=\cos\frac{1}{2}x, \\ 3) y=\frac{1}{2}\cos\frac{1}{2}x, \\ 4) Ox\downarrow1,Oy\leftarrow\pi.$

Answer 2

Building the Graph of y=2sin(2x+π/3)-2 and 1/2cos(1/2x-π/2)+1

To build the graph of the given functions, we can follow these steps:

1. Identify the Key Components of the Functions: - The given functions are: - y = 2sin(2x+π/3)-2 - y = 1/2cos(1/2x-π/2)+1

2. Determine the Amplitude, Period, Phase Shift, and Vertical Shift: - For the function y = 2sin(2x+π/3)-2: - Amplitude: 2 - Period: π - Phase Shift: -π/6 - Vertical Shift: -2 - For the function y = 1/2cos(1/2x-π/2)+1: - Amplitude: 1/2 - Period: 4π - Phase Shift: π - Vertical Shift: 1

3. Plot the Graphs: - Using the identified components, plot the graphs of the given functions on the coordinate plane.

4. Combine the Graphs: - Combine the graphs of both functions on the same coordinate plane to visualize their relationship.

5. Finalize the Graph: - Label the axes, title the graph, and provide any additional information necessary for clarity.

By following these steps, you can effectively build the graph of the given functions and visualize their behavior.

Let me know if you need further assistance!

Answer 3

Building the Graph of y=2sin(2x+π/3)-2 and 1/2cos(1/2x-π/2)+1

To build the graph of the given functions, we'll follow these steps:

1. Identify the Key Components of the Functions: - The first function is in the form y = 2sin(2x+π/3)-2. - The second function is in the form y = 1/2cos(1/2x-π/2)+1.

2. Plotting the Graphs: - We'll plot the graphs of both functions separately on the same coordinate system.

3. Graphical Representation: - The graph of y = 2sin(2x+π/3)-2 will represent a sinusoidal wave with an amplitude of 2, a period of π, a phase shift of -π/6, and a vertical shift of -2. - The graph of y = 1/2cos(1/2x-π/2)+1 will represent a cosinusoidal wave with an amplitude of 1/2, a period of 4π, a phase shift of π, and a vertical shift of 1.

4. Combining the Graphs: - We'll combine the graphs of both functions on the same coordinate system to visualize their relationship.

Let's proceed with plotting the graphs of the given functions.