10.3  Sum/Diff Formulas Cosine

Cosine Functions
      cos(a + b) = cos a cos b - sin a sin b
        cos(a - b) = cos a cos b + sin a sin b

  Cosine Function Highlights 

     Helpful hints:

  ~  Cosine functions (add or subtract two angles) will always start with cos x * cos x

  ~  If you are finding the sum of the angles, you will subtract the two products.

  ~  If you are finding the difference between the angles, you will add the two products.

  ~  You are trying to break down an angle you do not know and must find the exact value (no calculator), you should use the basic angles you learned earlier.

Using Cosine's Difference Formula to Find Exact Values  (Ex 2)

 ~  Determine what basic trig ratios can be used to change the unknown angle to angles we already know.

 ~  π/12 can be rewritten as the difference between 3π/12 and 2π/12 which should be reduced.

 ~   In this case, because we are subtracting the two angles, we will be using cosine's formula for the difference of the two angles.

In the next example (Ex 3), you are given an expanded form of either the sum/difference of sin/cos. 

  You need to determine what formula is given.  Is it cosine or sine?

   Once you determine that it is a difference formula for cosine, rewrite as the cosine of the difference between the two given angles.

   Simplify: do the math.