Sum, Difference, Double and Half Angle Formulas

We are proving (and practicing) with several important identities this week, all of them involving modifying the angles.  You must be able to generate a proof of them on your own, as well as using them to answer/simplify problems.

1/28  5.3  Sum and Difference Formulas
                  HW p.444/1-29 odd, 31-34, tan(A + B), tan(A - B)

1/29  5.3  More proofs of cos(A + B) and cos(A - B)
                  HW p.444-445/33-43 odd, 44,47,49,52,55,60,63-65,67

1/31  5.4  Double Angle Formulas
                  HW p.452/5-35 odd

2/01  5.4  Half Angle Formulas
                  HW p.451-452/39-47 odd, 51-53

2/04  Review

2/05  Test of 5.1 - 5.4

Fundamental Trig Identities

We return to the Demana book for our work with Trig Identities. Section 5.1 focusses on the Fundamental Identities - the ones you just have to know.  These include (but are not limited to) the cofunction, reciprocal, and Pythagorean identities.

1/18  p.430/1-29 odd, 31-34
1/22  p.430-431/35, 38, 41-45 odd, 59, 61, 67, 69-72

Core Set of Problems, etc.

Here are the Core Set of problems that you have to know how to do:
p.349/27, 28
p.354/22, 24
p.358/36-39

Here are two you should know how to do:
p.342/17
p.349/23
There is also an interesting suggested problem on the conference from James Zhang that relates the two together.

There will be something like:
p.343/19, 20;  p.353/15, 16
p.357/29-32

Another extra credit problem, due Friday 1/18 is p.349/29.

Mixed Applications (and the Goat)

We will be working on using our knowledge of Geometry as well as the trigonometric area formula, the Law of Sines, and the Law of Cosines to solve problems.  Some of the problems are difficult.  From the homework listed below, traditionally, at least one problem from 36-43 has been on the next test so you must know how to solve these problems.  We will be working on them in class too.

(Remember, we are using the Brown book.)
1/08  HW p.355-358/11, 14, 18, 21, 23, 29, 39, 40
1/10  HW p.356-358/20, 24, 25, 32, 36-38
1/11  HW p.357-358/33-35, 41-43

Also, for extra credit, you may do the infamous Goat Problem.
It is p.344/34 of the Brown book.  It is due on Monday, 1/14.

Law of Sines and Cosines

After working on a worksheet where the area formula for triangles evolved from trig applications (and some identities were derived), the homework moves to using trig for some geometric applications.  The next week of homework is from the Brown book.  We start with the Law of Sines, continue with the Law of Cosines and then mix it up with Mixed Applications.

1/04  read p.345, do p.347-349/1-27 odd
1/07  p.352-354/1-17 odd, 22

Return and Review

Welcome back from vacation.  Today we reviewed the fundamentals of trig functions.  This served as a refresher and a way to quickly set you up for any test corrections you need to make.  We also talked about inverses and started a packet that reminded you that reciprocals and inverses are not the same.  

HW:  finish the packet