1. Ch. 5 – Analytic Trigonometry
5.1 – Using Fundamental Identities

2. Reciprocal Identities:
Make a formula page in your notes for this chapter and put these facts on there!
Reciprocal Identities:
Quotient Identities:
Pythagorean Identities:

3. Cofunction Identities:
Make a formula page in your notes for this chapter and put these facts on there!
Cofunction Identities:
Even and Odd Functions
cos(-θ) = cos(θ) sec(-θ) = sec(θ)
sin(-θ) = -sin(θ) csc(-θ) = -csc(θ)
tan(-θ) = -tan(θ) cot(-θ) = -cot(θ)

4. Simplifying Trig Expressions
In this chapter, we will use trig identities to simplify/solve trig equations and find new identities.
To “simplify” a problem is to get rid of fractions and leave the fewest operations possible.
Recall our strategies for verifying trig identities:
Convert everything to sin and cos
Use a Pythagorean identity if you have a sin2 (or cos2, tan2, etc.) term
We will be adding more strategies throughout the chapter!

5. Simplifying Trig Expressions
Ex: Simplify the expression
Strategy #3: Factor out common terms
Strategy #2: Use a Pythagorean identity

6. Simplifying Trig Expressions
Ex: Simplify the expression
Strategy #4: Add terms by making a common denominator
Strategy #2: Use a Pythagorean identity

7. Simplifying Trig Expressions
Ex: Simplify
Strategy #5: Multiply the denominator by the conjugate
Strategy #2: Use a Pythagorean identity

8. Factoring Trig Expressions
Ex: Factor
Factor these like you would factor a quadratic!
Again, it’s just a quadratic!