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I think that you will be amazed if you know that proper mathematical equations of graphs shown above exist and the graphs shown above are obtained by plotting their mathematical equations. The software used for plotting and obtaining the graphs was Microsoft® Math of version 16.0.4023.0606 and having product id 79236-442-2177112-87011. I have personally entered equations in Microsoft® Math and obtained above mentioned graphs by plotting equations in Microsoft® Math. But, you will not have to enter the equations in Microsoft® Math because I am providing direct commands that can be entered in Microsoft® Math worksheet and graphs can be obtained by entering that command directly in Microsoft® Math worksheet input panel. Just copy and paste the commands given below in Microsoft® Math worksheet input panel and press enter to see the graph along with its equations. Note that equations and graphs both will be displayed in the window of Microsoft® Math after you enter the commands in Microsoft® Math worksheet input panel. Commands to obtain graphs shown above are given just below. But for these commands, please select 'Radians' instead of 'Degrees' in the angle measure drop down list in Microsoft® Math before plotting these commands to obtain exact graphs. In other words, set the angle mode to 'Radians' before using the commands.
The set of commands shown above is a very small subset of the set of total commands explored by me. In other words, more such different commands for different graphs have been explored by me. Click on the link given just below to see more such commands explored by me. The content given on the link given just below also includes information about commands for some most important graphs such as graphs of square wave, triangular wave, saw tooth wave etc.
There are infinite possibilities and opportunities available in exploring and finding new wonderful graphs and their commands. Hence I may continue to explore such commands in future and the commands explored by me in future will automatically appear in the sheet given just below.
HOW TO ANIMATE GRAPHS USING MICRSOFT® MATH
When you create a graph that involves unknown parameters (In a mathematical equation, a parameter is a constant that changes and results in a collection of related curves or surfaces. For example, in the equation y = mx+b, m and b are parameters), such as the graph of y = sin(ax), Microsoft Math initially picks an arbitrary value for the unknown parameter a and draws the graph using that value. After the graph is created, however, you can modify the value of a and animate the graph by using a range of values for the unknown parameter. What you see during the animation is a series of graphs, each drawn with a slightly different value of the unknown parameter. If your graph involves multiple unknown parameters, you can choose which parameter to animate. You can also set the values of some parameters to specific values while you animate another.
To animate a graph
- Expand Graph Controls.
- In the Parameter list, click the unknown parameter that you want to animate.
- In the Lower Bound box, enter a lower bound for the parameter. The default is 0.
- In the Upper Bound box, enter an upper bound for the parameter. The default is 2. (You can enter an upper bound that is smaller than the lower bound. In this case, Microsoft Math animates from the larger value to the smaller.)
- Click
To specify a particular value for the unknown parameter
- Expand Graph Controls.
- Move the slider to the value that you want to use.
To stop an animation
- Expand Graph Controls.
- Click
I have also used unknown parameter in some of the graphs such as a graph of line obtained from general equation of a line described in polar co ordinate system. Some graphs explored by me were obtained from more general equations and those general equations included unknown parameters. Changing the value of those unknown parameters will change the graph obtained which is called animating the graph. Animating parameters can give us deep insight into how a graph changes with those parameters. So you can watch different graphs by just adjusting different values of different parameters in the graphs involving different unknown parameters.
These were really amazing, thanks for sharing with me
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