This discussion focuses on identifying parametric equations from given graphs, specifically analyzing graphs labeled 1 through 3. The participant concludes that graphs 1 and 3 are not periodic and are excluded from being simple trigonometric functions due to their overall increase in both x and y. The equations for graphs E and F are derived as x = -2sin(t), y = -2cos(t) and x = sin(3t), y = sin(4t), respectively, which helps in matching them to the corresponding graphs. The discussion emphasizes the importance of recognizing symmetry and periodicity in graph analysis.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone interested in graphing parametric equations and understanding their properties.
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.