3. [40.18 Points] DETAlLS SCALCET9 10.1.EI.A.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Eleoncapt This module graphs parametric curves from several different families involving trigonometric and polynomial functions. In addition to the parametric curves themselves, graphs of x and y as individual function of tare shown. You can observe the behavior of the values of x and y as t increases and then watch how the parametric curve given by x = (it). y = g{t) is formed with these values working in tandem. Cycloids Select the third set of parametric equations. x = rtt sin(t)). y = r(1 - oos(t}). (a) Set r: 1 using the slider for r. The parametric curve can be visualized as the curve traced out by a point on the circumference of a rolling circle. If you vary r. what is the effect on the graph? 0 As r gets larger, the size of the arches in the curve remains constant. 0 As r gels larger, the size of the arches in the curve gets larger too. Q As r gets larger, the size of the arches in the curve gets smaller. (b) What parameter domain is required to draw one arch of the cyclold? 1. [-10.18 Points] DETAILS SCALCET9 10.1.AE.010. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example 4:)) Investigate the family of curves with the following parametric equations. x = a + cos(t) y = a tan(t) + sin(t) What do these curves have in common? How does the shape change as 6 increases? Solution We use a graphing calculator to produce the graphs for the cases a = 2, 1, 0.5, 0.1, O, 0.5, 1, 2 as shown in the figure. Notice that all of the curves (except the case a = C] ) have two branches, and both branches approach the vertical asymptote x = a as x approaches a from the left or the right. When a D , the branches become smooth again, and as a increases further, they become less curved. Notice that the curves with a positive are reflections about the -Seleot- c of the corresponding curves with a negative. These curves are called conchoids of Nicodemes after the ancient Greek scholar Nicodemes. He called them conchoids because the shape of their outer branches resembles that of a conch shell 0r mussel shell. 2. [-10.18 Points] DETAILS SCALCETQ 10.1.EI.A.001. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER lEIGoneapt This module graphs parametric curves from several dierent families involving trigonometric and polynomial functions. In addition to the parametric curves themselves. graphs of x and y as individual function of (are shown. You can observe the behavior of the values of x and y as tincreases and then watch how the parametric curve given by x = tit). y = 96} is formed with these values working in tandem Select the rst set 0! parametric equations. x = a coslbt), y = c sinldty (a) Set the equations to x = 2 cos\"). y = 2 sintt) using the sliders for a. b, c. and 0'. Describe the parametric curve. I This answer has not been graded yet. What minimum parameter domain is required to draw the entire circle? 0 S r