In addition to graphing and converting polar equations to rectangular equations from the previous post, there is one other type of equation you need to understand.
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 www.youtube.com/watch?v=BGWX0TOthsY&feature=youtu.be The files included with the beginning posts of this unit have some examples worked out. After you go over these types of problems, try the questions on the review sheet. The answer key was posted as well. Let me know what questions you have. If you are ready for it by Friday, I will give you a link to an assessment. You will have 24 hours to complete the test once I post the link. I would prefer to get it done by this weekend so we can start fresh with the next unit on Monday.. Otherwise, I will assign the test to be due by next Tuesday. Email any questions you may have. Per your mom, you also have a phone contact to which you may text messages. Don't be shy about asking questions and stay healthy..
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