sketching parametric equations worksheet

�Y�Kd��Ȓ�,�"y*��.$��a��\�D��k�1��O��+ú"O8�� >�,�1{��! Pre-Calculus Parametrics Worksheet Show work on separate paper. Look below to see them all. stream %PDF-1.5 For, if y = f(x) then let t = x so that x = t, y = f(t). Some of the worksheets below are Parametric Equations Worksheets – Graphing a Plane Curve described by Parametric Equations, Polar Coordinates and Polar Graphs, Area and Arc Length in Polar Coordinates with tons of interesting problems with solutions. Math Worksheets Videos, solutions, activities and worksheets that are suitable for A Level Maths. parametric equations that represent the same function, but with a slower speed 14) Write a set of parametric equations that represent y x . 1 0 obj CHAPTER 11 WORKSHEET PARAMETRIC EQUATIONS AND POLAR COORDINATES Name Seat # Date Review Sheet A SEE OTHER SIDE 1997 CALCULUS BC (a graphing calculator maybe used) 1. Then eliminate the parameter. x = f(t) = 6 t 2 y = g(t) = 2t 4 a. Plotting a parametric curve: Find the position of the robot You will ﬁnd the original discussion worksheets and their solutions on the Math 241 course webpage. &^G�M�p��.V��#��.��=��q�j�װV�~�v��=��j��g�oA�� j��?RՀy��[��Q��j�y؋S�Q�-z��d��U��v�x��a�8q��qT�s#c��n/��K4��r~��Ӌ��k�z���?��x.��&1�(-@&��-��Nia!�b��n�'\GۡU��#0Mpx��>��1�,��N`f�U�s~я�@�ur��=�F� *�wi Once matched, there will be 10 sets of thre Any strategy we may use to find the parametric equations is valid if it produces equivalency. endobj 2. x = 6 – t 3. x = ½t + 4 4. x = 3 cos t y = 3t - 4 y = t3 y = 3 sin t 5. In what direction is the graph traced out as the value of t increases? Thursday,August30 ⁄⁄ Parametric curves deﬁned using vector arithmetic. Displaying top 8 worksheets found for - Graphing Parametric Equations. F�o�+�i Parametric Equations. x��]�r5�w��a.�2ѿF[��lA��"��x��؉}R��w�n��H��Fs�wY�uN�S��ӟ�/�|��_w�|��紣�{��v��Ӓ�Tu/��g�{kK�/��{��w ��K�^��IAT�^$�vOHO��^\��=�(�R��H�[��{�@E��k��p �^>t{:�~�O��n�v��^綾� Most common are equations of the form r = f(θ). This method is referred to as eliminating the parameter. Once you find your worksheet (s), you can either click on the pop-out icon or download button to print or download your desired worksheet … Then substitute this result for the parameter in the other parametric equation and simplify. A sketch of the parametric curve (including direction of motion) based on the equation you get by eliminating the parameter. <> Taking too long? Intro to Velocity and Area - Relationship between velocity, position, and area. <>>> WORKSHEET 13.4-1 Pg 11 Obtain the rectangular equation by eliminating the parameter. Parametric Equations of Lines on a Plane x = 4 – 2t y = 5 + 3t (a) Use a table of values with three values of t to plot the graph. Sketch the graph determined by the parametric equations. Previous Section: Trigonometry (Part 2) ... (due to nature of sketching digitally – this may change with collaboration with Desmos) Key Skills. <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Make a table of values and sketch the curve, indicating the direction of your graph. Solution We again start by making a table of values in Figure 10.2.2 (a), then plot the points ( x , y ) on the Cartesian plane in Figure 10.2.2 (b). 1. Parametric equations for cycloid Table 0 sketch -axes, plot points, draw curve through them one arch of the cycloid Drawing Graphs of Parametric Equations using Maple Command form: plot([ -expression, -expression, parameter range],scaling=constrained); Show graph of parametric equations 4. cos t - 2 Sinat 4 + 3tan t 2 sect 3 cos t 3 sin t 4 sec t - 3 tan t 3t -4 4 sin (2t) - 2 cos (2t) 4+ 2 cost b) Give an appropriate … Check your work by first graphing the parametric equations (on your calculator) than graphing the i) Plot U against T for Ft Q P Q táP Ð : Point P has the value P Make a table of values and sketch the curve, indicating the direction of your graph. Parametric Equations Name 1. Use this fact to help sketch the curve. endobj endobj x=f(t) and y=g(t) give the position curve as parametric equations. Parametric Equations Name 1. Graphing Parametric Equations and Eliminating the Parameter Ex. (b) Using the factored form (and your technique from Problem 3) sketch this object in R3. endobj They are mostly standard functions written as you might expect. a) Find the position of the particle when t = 2 5. Fill in the table and sketch the parametric equation for t [-2,6] t x y -2 -1 0 1 2 3 4 5 6 x = y = 2 – t. Problems 2 – 6: Eliminate the parameter to write the parametric equations as a rectangular equation. %PDF-1.5 Limits on x x and y y. Read more. A range of t t ’s for a single trace of the parametric curve. Parametric Equations Worksheet - Answer Key I II III IV-2 2 1. 3 0 obj Then write a second set of parametric equations that represent the same function, but with a faster speed and an opposite orientation. <> 2. x = 6 – t 3. About: Beyond simple math and grouping (like "(x+2)(x-4)"), there are some functions you can use as well. Although we have just shown that there is only one way to interpret a set of parametric equations as a rectangular equation, there are multiple ways to interpret a rectangular equation as a set of parametric equations. 2. x = 3 – 2t y = 1 + 2t Ans: Linearly, up to the left 2. 1 0 obj y - … As an example, the graph of any function can be parameterized. <> Note that the parametric equations of the curve obey both z(t) = x(t)2and x(t)2+ y(t)2= 1 … Select some values of on the given interval. During the time period t = 0 to t = 6 seconds, a particle moves along the path given by x tt t3cos S and y t 5sin S . x��]͎�6�70��cw��j�� @ b '��mϮg��t`��ݖERݒ��~�� HE~��U��g�=��f�_�/��=��'�^?��~��լ�j��p�l#�Ǜ�ϟ��\�X�Ř�T��W�a�Q�Q��ӭf_�c?�?��ٳ�b��̺�p��}?�H�o�3]W�Y�� g\;�ٽ��p{��?O��|��'��?��=�?F��R�Wy��K:1*or%6�[Yo b�� D��-��n>"��Q�(^e>��֏Ds�=�V�U|F�u�ﺲ�qWWV1�}\�z�Ɉ�4N��ʊ)3pIn6��D��zG��vzsd��߼'�+�h�pO��_�+{O/�Л ��E��큋��ڝ�c��Zd~��z��Yvb�f��}Y��2?9"�v�{�+=��O�f>YW��YӀ��V��|H+��'��l�kS9��Q�u��kW��Ϸ��m. Q1: Noah wants to graph the parametric equations = 2 − 2 and = 3 − , where 0 ≤ ≤ 2 . 3 0 obj The Definite Integral. 4. <>>> EXAMPLE 10.1.1 Graph the curve given by r … ��$X��>T�ixБ~�8�,:s,u�E0��柉��h��Yhb!Y=�؎��'T� �\. Sketch the graph of x = sin2(t), y= cos(t) for 0 t ˇin (II). }��> ��ah��!|`�ކ��WT�� Do not use your calculator. 2 0 obj Pre-Calculus Parametrics Worksheet Name 1. How to convert from Parametric to Cartesian form and find the area under a parametric curve? 1) Sketch the parametric curve for the following set of equations T L P 6áU L wP Esá Ft Q P Q t [2] 2) Eliminate the parameter from the following set T L tP 6 Ev U L P Es [1] 3) A curve , % , has the parametric equations T L P 7 FxPáU L P 6 where P is a parameter. Core 4 Maths A-Level Edexcel - Parametric Equations (1) An introduction to parametric equations. Bridge to Calculus 1 Parametric Practice 1. is a pair of parametric equations with parameter t whose graph is identical to that of the function. %�� 2 0 obj For the curve (x + 5)2 + y2 = 4 complete the following: a) Write a pair of parametric equations for the curve. Sketch a graph using either the parametric equations or the rectangular equation 1-1-1. y - 1+1 2 X-2-5. Fill in the table and sketch the parametric equation for t [-2,61 Problems 2 - 11: Eliminate the parameter to write the parametric equations as a rectangular equation. t is time in seconds after we begin to watch the robot ; x and y are in feet We designate the time at which we start observing the robot as t = 0 sec. WORKSHEET ON PARAMETRIC EQUATIONS AND GRAPHING Work these on notebook paper. Describe the how the numbers 1, ½, and 3 in the following parametric equations transform the graph from part (a). View 449240364-D06-Parametric-Worksheet-doc.doc from CALCULUS 3 at Indiana University, Bloomington. 4 0 obj Fill in the table and sketch the parametric equation for t [-2,6] 2x = t + 1 y = 2 – t Problems 2 – 6: Eliminate the parameter to write the parametric equations as a rectangular equation. For each value of use the given parametric equations to compute and 3. <>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 2. x = 6 – t 3. x = ½t + 4 4. x = 3 cos t y = 3t - 4 y = t3 y = 3 sin t 3��RIj��6��@��|ve �|�}m7}t��a��X��a@�]0��=:�[�� /vl�__��f�,��]^Xo��x��ّ��O*��C�eQ��&��D`ȑ��]ܣG��m�P��tx�� Then eliminate the parameter. All other problems come from the regular Math 241 worksheet, although I may have modiﬁed them slightly. Prior content: AS Co-Ordinate Geometry. endobj x = ½(t + 1) and y = = (t( + 3. ��i To see the full index of tutorials go to ExamSolutions at http://www.examsolutions.co.uk stream This precalculus video provides a basic introduction into parametric equations. 1. Graphing a plane curve represented by parametric equations involves plotting points in the rectangular coordinate system and connecting them with a smooth curve. 18. In what direction is the graph traced out as the value of t increases? Page 2 2. The number of traces of the curve the particle makes if an overall range of t t ’s is provided in the problem. endobj Sketch the graph of the parametric equations x = cos 2 ⁡ t, y = cos ⁡ t + 1 for t in [0, π]. Fill in the table and sketch the parametric equation for t [-2,6] x = t2 + 1 y = 2 – t Problems 2 – 6: Eliminate the parameter to write the parametric equations as a rectangular equation. Conversely, given a pair of parametric equations with parameter t, the set of points (f(t), g(t)) form a curve in the plane. Curve sketching can be less tedious by converting the two parametric equations into one rectangular equation. )�>uٻ?p�I�ಥd1��b�0�Ř�,��bi� Sketch the graph determined by the parametric equations. �л��n\�e��8ǹ8�U��r\��5��VTvU:��n�8�.�jZ޾ڡ�twk��h݈0i9vkp��s�0n�Ǿt5��_d�֓��"�F֓�X&��>�t�f �sG$o��{0 �(�ٽ��>s�dy��p~�x/:3:��L��=5v�Ϻ[�� NT��~��ʹ�L Parametric Equations Name 1. Note: Problems marked with an asterisk (*) are Merit problems. Sketch the graph of x= cos(2t), y = sin(2t) for 0 t ˇ 2 in (I). �3fzBS��B�l�H�,�*��)_��nl��V�ah�L��*қFQ�ZE%g��g�,k�c�U��X#)��go>��g]�"�b1 @>��5c�_�~�H��!��)�u��%n��?��{��y��s+a?��vSC{)b�R�3�X�&n��:@PԻ�Eϯo �o��[[>\텷� f�>�ܔ��2t�6�t�뫛;�,��ߏ#r}��&��:m�H ��8\vp��F�]��%[�m _�@z�u��Q�p}�A�7�'�z�̮{Y�e�s��\�z��X�a_(��R- �X�3/%/RH�B!��׆Q��}�0G�Y��R�ڟ�� B��"�b~`I�>0�fQz�� /��_��_�� 2��c�X_�{*}�,��i�Ѓ�q� ��tF��Q�+�� JFS�R"z��~��O�AM{ފ ��D�_wz�am>��QVӪl枪�J�ȷ@�"�_�8xx,��{8[J?�>gs0<8��o�� C��&M�u�Lӹ[O��"lևC��e�)B0 ��AI��6��ńD��ѣh1�@ m=J��Ԥ�Ki��T�}Z� �`�}Z�R s&�k�`�͢h�\1�%�TԂQ�h !'�0�.-Ȅ�0Xѥ��i�(�4. <> 4 0 obj 1. x t y t 2 1 and 1 2. x … (a) x t y t 1, 2 _____ (b) x t y t t d d2 3, 2 , 2 3 _____ (c) x t y t 3 2cos , 1 3sin Homework: Worksheet and AP Review 34 x y To eliminate the parameter, solve one of the parametric equations for the parameter. Curve sketching parametric equations. 2. Write a pair of parametric equations which will move the graph in part (a) 4 units to the left and three units down. Name 1. In this worksheet, we will practice graphing curves given by a pair of parametric equations in 2D. Fill in the table, plot the points, and sketch the parametric equation for t [-2,6] x = t2 + 1 t y = 2 – t -Problems 2 – 10: Eliminate the parameter to write the parametric equations as a rectangular equation. Show that the curve with parametric equations x= sin(t), y= cos(t), z= sin2(t) is the curve of intersection of the surfaces z= x2and x2+ y2= 1. Fill in the table and sketch the parametric equation … %�� Some of the worksheets for this concept are Parametric equations work, Parametric equations, Bridge to calculus 1 parametric practice, Pre calculus parametrics work 2, Parametric and polar curves, Chapter 22 parametric equations, Ideal projectile motion, Ap calculus bc name chapter 11 work parametric. 240 Chapter 10 Polar Coordinates, Parametric Equations Just as we describe curves in the plane using equations involving x and y, so can we describe curves using equations involving r and θ. Graphing a Plane Curve Described by Parametric Equations 1. … Consider the set of points in R3 deﬁned by the parametric equation l(t) ˘(¡5¯2t,2¯3t,1¡t) for all t. (a) Using the properties of vector arithmetic, factor l(t) into the form p¯tvwhere pand vare vectors in R3.