HallsofIvy said:1 and 3 are clearly not periodic- x and y both have an overall increase. That tells you that they are not simply trig functions and that excludes A, B, C, and G. They do appear to have a symmetry about the line y+ x= some number. D is not symmetric so that's excluded leaving only E and F which, because of the "t" added increase steadily as t increases. Subtracting off that "t" is the same as rotating the x= y= t line to the x-axis:
E then becomes x= -2sin(t) and y= -2cos(t) while F becomes x= sin(3t) and y= sin(4t). It should be easy to see which of those 1 and 3 correspond to.
Parametric equations are a set of equations that express a quantity in terms of one or more independent variables, typically represented by t. Unlike regular equations, parametric equations use a different variable for each quantity, allowing for more complex and dynamic relationships between variables.
Parametric equations are graphed by plotting points that correspond to values of the independent variable, t. These points are then connected to create a curve or shape that represents the graph of the parametric equations. The more points plotted, the more accurate the graph will be.
Parametric equations are commonly used in fields such as physics, engineering, and computer graphics to model and understand complex relationships between variables. They can also be used in motion tracking and animation, as well as in designing and analyzing curves and surfaces in 3D space.
Yes, parametric equations can be used to graph functions that cannot be represented by regular equations, as they allow for more flexibility in representing complex relationships between variables. This makes them useful in visualizing and understanding a wide range of mathematical and scientific concepts.
While parametric equations can be powerful tools for graphing and analyzing complex relationships, they can also be more difficult to work with compared to regular equations. They may also require more computational power and time to graph, especially for large datasets. Additionally, parametric equations may not always provide a complete or accurate representation of a function or system.