The last type of equations to review are parametric equations. A parametric equation is similar to the normal rectangular equations with x's and y's, except they have an extra parameter (variable) for time - (t). It is generally used to track the course of an object along some kind of path (this is an equation in terms of x and y coordinates) but the t tells where the object is located on the path at a give time t: - Think of tracking the path of an asteroid or comet as it passes through the solar system. The entire track of the comet is generally described by the equation of an ellipse, but the t component tells where the comet is on this elliptical path at time t. When converting from parametric to rectangular equations, you want to be able to get rid of all the t's in the equations. The main techniques are to either 1) Rewrite one of the equations to get t by itself on one side with all the x's and y's on the other. Then then use that value for t in terms of x and y as a substitute in the second equation to replace all ts. 2) If you have sin t and cos t and you want to get a t by itself, you will often need to write in terms of the identity (sin t)^2 + (cos t)^2 = 1. And then do a suitable substitution for t. Some helpful videos: Graphing parametric equations with the TI 84 www.youtube.com/watch?v=4Y14XhPD7Os Converting parametric equations to rectangular form www.youtube.com/watch?v=tW6N7DFTvrM Converting parametric equations of a line into a rectangular equation (problem 24) www.youtube.com/watch?v=BGWX0TOthsY&feature=youtu.be Included below is a pdf file with some notes showing examples worked out, a pdf file of the review sheet for the entire unit, and the pdf files of the answer keys for the homework and review sheet. Your homework from the book pages is: Page .807: 2, 5, 6, 8, 11, 14, 16, 24 Problem 24 is just like one of the problems explained in the class notes included. Your second part of the homework is the review sheet listed below. Both assignments should be completed by Thursday, 4/16/20. Your FIRST ASSESSMENT for the 4th quarter will be due at the end of Friday 4/17/20. The link will be posted Friday morning by 8:00 a.m. You will have until midnight 12:00 a.m. on Saturday, giving you a 16 hour window in which to complete it. After that, the assessment will be locked. Please note that once you submit this exam, you will not be allowed back in to submit it again. As always, email me with any questions.
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