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Developing Expert Voices Pre Calculus 40S enriched 2007 My name is Sandy and I like the colour purple.  DEV PROJECT

Problem One ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (a) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (a) ,[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (a) ,[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (b) ,[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (b) ,[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (c) ,[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem One – answers (c) ,[object Object],[object Object],[object Object],DEV PROJECT

Problem Two ,[object Object],[object Object],DEV PROJECT Please note that for tests or examinations, add arrows and label your axis.

Problem Two – answers (a) ,[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Two – answers (a) ,[object Object],[object Object],DEV PROJECT

Problem Two – answers (a) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Two – answers (a) ,[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Two – answers (a) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Two – answers (b) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Two – answers (b) ,[object Object],DEV PROJECT

Problem Two – answers (c) ,[object Object],DEV PROJECT

Problem Two – answers (c) ,[object Object],DEV PROJECT Don’t forget to add an asymptote where the graph has zero(s) or where x = 0.

Problem Three ,[object Object],DEV PROJECT

Problem Three - answers ,[object Object],DEV PROJECT We basically expanded the problem. We know that COT is the reciprocal of tan and instead of tan, you can use sin and cos. We also changed 1 to sinΘ/sinΘ because that equals one. So we don’t necessarily add anything to the original question.

Problem Three - answers DEV PROJECT Here we simply just multiplied everything out. Just like we were doing before, to get rid of the double fraction we multiplied the numerator by the reciprocal of the denominator. The sinΘ’s reduce!

Problem Three - answers DEV PROJECT You then end up with this after you reduce! You’re probably wondering how the heck does cos 2 Θ equal 1-sin 2 Θ? Well, knowing our identities: sin 2 Θ + cos 2 Θ = 1 If we rearrange the order, we can see that cos 2 Θ = 1-sin 2 Θ If you notice, 1-sin 2 Θ is a difference of squares. SO, it is easily factorable.

Problem Three - answers DEV PROJECT The 1-sinΘ’s reduce. And you’re left with 1+sinΘ! Q.E.D *When You’re finished solving, you must always put Q.E.D to indicate that you are finished.

Problem Four ,[object Object],[object Object],[object Object],DEV PROJECT

Problem Four – answers(a) ,[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Four – answers(a) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

Problem Four – answers(a) ,[object Object],[object Object],[object Object],[object Object],DEV PROJECT These reduce.

Problem Four – answers(b) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],DEV PROJECT

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