12.6.1 Reciprocal and Pythagorean Identities

Resources:

• Notes: 6.1 Reciprocal, Quotient and Pythagorean Identities

Assignment

• p297 #1-8, 10, 11, 13, 14, C1 C2 *16 *17

Things you should know after today:

• know how the Pythagorean Identities are derived

Attachments:

File	Description	File size
12.6.1.notes.pdf		450 kB

12.6.2 Sum and Difference Identities

Resources:

• Notes: 6.2a Sum and Difference Identities
• Notes: 6.2b Double Angle Identities

Assignment

• p306 #1, 12, 6-10, 17, 19
• Example from notes
• p306 #3-5, 11, 12, 13, 15, 16

Things you should know after today

Attachments:

File	Description	File size
12.6.2a.notes.pdf		398 kB
12.6.2b.notes.pdf		442 kB

12.6.3 Proving Identities

Some points to remember:

• Set up your "Berlin Wall"
• Strategies to apply:

1. Replacing known identities
   1. Second degree terms -> Pythagorean Identities
   2. Double Angle Identities should be converted to single angles
   3. Rewrite things in terms of sine and cosine if necessary
2. Simplifying complex fractions (fancy 1) or combining fractions (common denominator)
3. Look for GCF's or factors that can be reduced
4. Look for Binomial conjugates.  Often you can use a "fancy 1" on one side of the wall to make a difference of squares that will turn into a Pythagorean Identity

Resources:

• Notes: 6.3(a abd b) Proving Identities

Assignment

• p314 #1-7 C1 C2
• p314 #9-15

Attachments:

File	Description	File size
12.6.3.notes.pdf		243 kB

12.6.4 Using Identities to Solve Equations

Resources:

• Notes: 6.4 Solving Trigonometric Equations Using Identities

Assignment

• p320 #1-5 7-12 15

Attachments:

File	Description	File size
12.6.4.notes.pdf		271 kB