Lesson Map
Use this table as your route through the unit. Lesson numbers jump directly to the matching explanation.
| Lesson | Topic | You should be able to… |
|---|---|---|
| 7.1 | Fundamental Identities | Use reciprocal, quotient, and Pythagorean identities as equivalent forms. |
| 7.2 | Simplifying Trigonometric Expressions | Choose substitutions that reduce an expression to a simpler form. |
| 7.3 | Verifying Identities | Transform one side of an equation until it matches the other side. |
How the Unit Is Built
Each resource below is part of the same learning cycle. Select a card to jump to it.
Content Summary
Work through these lessons in order. Focus on the meaning of the mathematics, the decision that selects a method, and a check that confirms the result.
Fundamental Identities
Use reciprocal, quotient, and Pythagorean identities as equivalent forms.
Simplifying Trigonometric Expressions
Choose substitutions that reduce an expression to a simpler form.
Verifying Identities
Transform one side of an equation until it matches the other side.
Video Library
These links open focused video searches by lesson topic. Use them as reinforcement rather than as a substitute for showing your own reasoning.
Fundamental Identities
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Simplifying Trigonometric Expressions
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Verifying Identities
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Vocabulary
These terms should appear naturally in explanations, diagrams, and written reasoning.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Sample Problems
Try each problem before opening the solution. The examples are original practice aligned to the unit skills.
Simplify
Show solution
Simplify
Show solution
Pythagorean
Show solution
Derived identity
Show solution
Verify
Show solution
Strategy
Show solution
Equations & Rules
Know what each relationship means and when it applies; do not treat the box as a list of disconnected formulas.
Review Guide
Skill Checklist
- I can use reciprocal, quotient, and Pythagorean identities as equivalent forms.
- I can choose substitutions that reduce an expression to a simpler form.
- I can transform one side of an equation until it matches the other side.
How to review
- Complete the unit Skills Check packet without notes.
- Mark the exact skill behind each error.
- Return to that lesson and complete a fresh example.
- Explain the correction in words, then retry a similar problem.
- Finish with mixed practice so you must choose the method yourself.
Performance Task
Identity Strategy Guide
Create a visual decision guide that shows when reciprocal, quotient, and Pythagorean identities are useful. Support each branch with an original example and verification.
Evidence to include
A labeled mathematical model, organized calculations, appropriate units and precision, a written interpretation, and a check or discussion of limitations.