1. C4 Chapter 2: Parametric Equations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 19 th November 2014

2. Parametric vs Cartesian Equations  A parametric equation is one where each of x, y (z etc.) are expressed in terms of some independent parameter.

3. Sketching Parametric Curves t-3-20123 x9410149 y-6-4-20246 Let’s just try a few values for the parameter and see what coordinates we get... ? 2 4 6 8 6 4 2 O -2 -4 -6 ?

4. Solving Problems involving Parametric Equations ? ? ? Q Q

5. Test Your Understanding C4 Jan 2013 a ? b ?

6. Exercise 2B 1 a c e 2 a c e 5 7 8 9 10 a b ? ? ? ? ? ? ? ? ? ? ? ?

7. Converting from Parametric  Cartesian We can use substitution or well known identities to convert parametric equations into Cartesian ones. This involves eliminating the parametric variable and forming a single equation. ? ?

8. Test Your Understanding C4 June 2013 ? C4 Jan 2011 ? which double angle formula would be best here?

9. Exercise 2C C4 June 2012 Q6 ? Harder! C4 Jan 2008 Q7 ? 3 4 5 c e g i ? ? ? ? ? ? ?