Math 152 Lab 5 - ExercisesExercisesü Assignment 1: Plotting Parametric CurvesInvestigate the following family of parametric curves: xHtL = a cos HtL + cosHatLyHtL = a sin HtL + sinHatL-p§t§pYour answer should include:è A plot of the curve for a = 2. è A plot of the curve for a =-2.è A plot of the curve for a = 3.è A statement of the curves' behavior as a gets larger and larger. Use of the Manipulate command could make this more obvious..In[18]:=ü Assignment 2: A Comparison of CurvesCompare the curve xHtL = 6 cos HtL + 5 cosH3 tLyHtL = 6 sin HtL - 5 sinH3 tL0§t§2pwith the curve xHtL = 6 cos H2 tL + 5 cosH6 tLyHtL = 6 sin H2 tL - 5 sinH6 tL0§t§pYour answer should include:è A statement of the difference(s) between the two curves, if any.è An explanation why any differences or similarities are present.In[19]:=ü Assignment 3: Animating a Parametric CurveLissajous curves are the types of curves that appear in oscilloscopes, a type of measurement equipment used in physics andelectronics. They are of the form: xHtL = cos HatLyHtL = sin HbtLInvestigate these types of curves. Your answer should include:è A statement of what occurs when a = b.è A plot of the case when a = 3, b = 5, and 0 § t § 2 p.è An animation of the above curve being drawn produced using Manipulate.In[20]:=ü Assignment 6: Polar PlotsCreate plots of the following polar curves:è rHqL = 1 + cosIq2M, 0 §q§4 pè rHqL = 1 - 2 sinH3 qL, 0 §q§2 pè rHqL =‰q10, -20 §q§20è rHqL =‰cosHqL- 2 cos H4 qL + IsinIq12MM5,0 §q§24 pYour answer should be the four plots.In[23]:=ü Assignment 8: The Polar Rose - Optional (bonus credit)Investigate the following family of curves:rHqL = cosHm qL, 0 §q§2 p, m = 1, 2, 3, ...Your answer should include:è Plots for the values m = 1, 2, 3, 4, 5, and 6.è A statement of what happens as m increases. (Use of Manipulate with m as the parameter may help here)è An explanation why sometimes an increase in m causes the figure to become more simple instead of more complicated.è Animations are not required, but may be helpful in figuring out what is going on.In[25]:=2 Math 152 Lab 5