PreCalculus
Chapter 3 Trigonometric Identities
Unit 3-1 Proving Trigonometric Identities
- Standard 3a:Prove basic Trigonometric Identities and use them to simplify Trigonometric equations
Agenda
- Trigonometric Identities
- Pythagorean Identities
- Assignment 3-1: Pg 127 #1, 2, 5-13 odd
Unit 3-2 Trigonometric Identities & Factoring
- Standard 3b: Factor polynomials using grouping and sum/difference rules
- Standard 3c: Prove trigonometric identities that involve factoring.
Agenda
- Screencast Review: Rules to Remember
- Factoring by Guess & Check
- Factoring by Grouping
- Factoring to Simplify Rational Expressions
- Factoring Practice (pdf plus ones from keynote)
- Desmos Activity
- Assignment 3-2: Part A Pg 136 #1-8 Part B #9-10, 12, 14
Unit 3-3 Composite (Sum & Difference) Identities
- Standard 3d: Find exact trigonometric values for composite arguments.
- Standard 3e: Solve equations involving composite argument rules.
- Standard 3f: Prove identities involving composite rules.
Agenda
- Composite (Sum and Difference) Identities for Sine and Cosine
- sin(A + B) = sinAcosB + cosAsinB
- sin(A – B) = sinAcosB – cosAsinB
- cos(A + B) = cosAcosB – sinAsinB
- cos(A – B) = cosAcosB + sinAsinB
- Using the Composite Identities to find missing angles
- Using the Composite Identities to find trigonometric values
- Assignment 3-3: Part A Pg. 145 #1 a) b), 2 a) b) Part B 3, 4, 5, 8, 10
Unit 3-4 Double Angle Identities
- Standard 3g: Find exact trigonometric values for double angle trigonometric functions.
- Standard 3h: Solve equations involving double angle rules.
Agenda
- Double Angle Identities
- sin(2A) = 2sinAcosA
- cos(2A) = cos2A– sin2B
- cos(2A) = 2cos2A – 1
- cos(2A) = 1– 2sin2A
- Assignment 3-4: Pg. 151 #1, 2, 4, 9
Unit 3-5 Half Angle Identities
- Standard 3i: Find exact trigonometric values for half angle trigonometric functions.
- Standard 3j: Solve equations involving half angle rules.
Agenda
- Assignment 3-5: Pg 153 #1, 2, 3, 6-9 Part B #12-15
Unit 3-6 Solving Equations with Identities and Algebra
- Standard 3k: Solve mixed trig identity problems using algebraic substitution
Agenda
- Solving problems that have mixed trig identities
- Using straight algebraic substitution to simplify
- Assignment 3-6: Pg. 170 #1, 2, 3, 7, 8, 9, 10, 18, 22