Graph y=-sin2(x-(3.14/4))
To graph the equation y = -sin(2(x - π/4)), we can start by understanding the properties of the sine function.
The general form of the sine function is y = A*sin(B(x - C)) + D, where A, B, C, and D are constants that affect the amplitude, period, phase shift, and vertical shift of the graph, respectively.
In our given equation, y = -sin(2(x - π/4)), we have:
A = -1, which represents the amplitude (the vertical distance between the maximum and minimum points)
B = 2, which represents the frequency or number of complete cycles within a specified interval
C = π/4, which represents the phase shift (horizontal shift of the graph)
D = 0, which represents the vertical shift
Now, let's analyze these properties in order to graph the equation:
1. The amplitude (A) is -1, which means the graph will be reflected about the x-axis compared to the basic sine function.
2. The frequency (B) is 2, meaning the graph will go through two complete cycles within the interval of 2π (one full period).
3. The phase shift (C) is π/4, indicating the graph will be shifted to the right by π/4 units.
4. The vertical shift (D) is 0, meaning the graph will not be shifted vertically.
To graph the function, follow these steps:
1. Choose a suitable interval for the x-axis. For example, let's use -2π to 2π, which covers one full period of the function.
2. Divide the chosen interval into multiple equal parts. For precision, you can divide it into 10 or more parts.
3. Calculate the corresponding y-values for each x-value using the equation. Plug in each x-value into the equation y = -sin(2(x - π/4)) to find the y-coordinate.
4. Plot the obtained coordinates (x, y) on the graph.
5. Connect the plotted points smoothly to form the graph.
Remember to label the axes accordingly and indicate any important points (such as maximums, minimums, and intercepts) to make the graph comprehensive.
By following these steps and applying the provided equation properties, you should be able to graph y = -sin(2(x - π/4)).