Ch. 5 – Analytic Trigonometry 5.1 – Using Fundamental Identities

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

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)

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!

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

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

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

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