Trig Identities & Equations

Essential question: How can we use and solve trig functions to predict future outcomes?

8.1 Trig Identities

- Explanation:
  - - Notes | Annotated

- - All of the trig identities and equations
    - Khan video: Intro to the Pythagorean trig identity
    - Khan video: Proof of the Pythagorean trig identity
    - Khan video: Using the Pythagorean trig identity
    - Khan article: Pythagorean identity review

- Practice:
  - - Khan exercise: Use the Pythagorean identity
    - Worksheet #1 | Answers
    - Worksheet #2 | Answers

- - Trig Identities Quizlet Flashcard

8.2 Simplify Advanced Trig Expressions Using Pythagorean Identities; Symmetry and periodicity identities

Explanation:
- Notes | Annotated
- Khan video: Examples using Pythagorean identities to simplify trigonometric expressions
- Khan video: Sine & cosine identities: symmetry
- Khan video: Tangent identities: symmetry
- Khan video: Sine & cosine identities: periodicity
- Khan video: Tangent identities: periodicity
Practice:
- Worksheet #1 | Answers
- Worksheet #2
- Khan Exercise: Manipulating trig expressions with Pythagorean identities

8.3 Solve Trig equation with one trig ratio without a calculator

- Explanation:
  - Notes | Annotated
    - Khan video: Example: Graph of cosine
    - Khan video: Symmetry of trig values
- Practice Problems:
  - - Worksheet #1 | Answers

8.4 Solve Trig equation with one trig ratio using a calculator

Explanation:
- Notes
  - Khan video: Solving sinusoidal equations of the form sin(x)=d
  - Khan video: Solving cos(θ)=1 and cos(θ)=-1
Practice Problems:
- - Khan exercise: Solve sinusoidal equations (basic)
  - Khan exercise: Solve sinusoidal equations
  - Worksheet #1 | Answers
  - Worksheet #2 | Answers (all degrees)
  - Worksheet #3 | Answers (all radians)

8.5 trig function work problems

Explanation:
- - Word Problems Exact Answers Notes | Annotated
  - Word Problems Approximate Answers Notes | Annotated
  - Khan video: Trig word problem: solving for temperature
  - Khan article: Trigonometric equations review
Practice Problems:
- - Khan Exercise: Sinusoidal models word problems
  - Word Problems Exact Answers Worksheet (A calculator is not allowed on this section so use the unit circle.)
  - Word Problems Approximate Answers Worksheet (A calculator is allowed.)

8.6 Solve trig equations when there is more than one trig ratio

- Explanation:
  - Notes | Annotated
- Practice Problems:
  - - Worksheet #1 | Answers
  - Worksheet #2

8.7 Solve trig equations with identities

Explanation:
- - Notes | Annotated
  - Khan video: Example: Intersection of sine and cosine
Practice Problems:
- - Worksheet #1 | Answers

8.8 Solve by Graphing

Explanation:
- Notes
Practice Problems:
- Worksheet

Review

Explanation:
- Summary Notes | Annotated
- Khan article: Trig identity reference
Practice Problems:
- Worksheet #1

More identities:

Sum and double angle identities

Explanation:
- Khan video: Finding trig values using angle addition identities
- Khan video: Using the cosine angle addition identity
- Khan video: Using the cosine double-angle identity
Practice Problems:
- Khan exercise: Find trig values using angle addition identities
- Khan exercise: Using the trig angle addition identities

Difference and half angle identities

Explanation:
- Khan video:
Practice Problems:
- Khan exercise:

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