Section 5.1 - Fundamental Identities

Essential Question(s): 

Explain how identities can be used to simplify expressions and solve trigonometric equations.

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Identities

• What are trig identities? (pg 444)
  
• What is the domain of validity? (pg 444)

Basic Trigonometric Identities

• Review the basic trig identities. (pg 445)

Pythagorean Identities

• What are the pythagorean identities? (pg 446)
• How can you use the identities without a calculator? (Ex 1 pg 446)

Cofunction Identities

• What are the cofunction identities? (pg 446-447)

Odd-Even Identities

• What are the Odd-Even identities? (pg 447)
• How can you use the identities? (Ex 2 pg 447)

Simplifying Trigonometric Expressions

• How do you simplify by factoring and using identities? (Ex 3 pg 448)
• How do you simplify by expanding and using identities? (Ex 4 pg 448)
• How do you simplify by combining fractions and using identities? (Ex 5 pg 448-449)

Solving Trigonometric Equations

• How do you solve a trigonometric equation? (Ex 6 pg 449)
• How do you solve a trigonometric equation using factoring? (Ex 7 pg 450)
• How do you solve a trigonometric equation using a calculator? (Ex 8 pg 451)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 444 - 451.
• Make sure to read the paragraphs between the examples.

Trigonometric Identities

Simplifying Trig Expressions

Pythagorean Identity Practice

Simplify Trig Expressions Practice #1

Simplify Trig Expression Practice #2