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… |
|---|---|---|
| 4.1 | From Unit Circle to Sine | Track the y-coordinate as an angle rotates to create y=sin x. |
| 4.2 | From Unit Circle to Cosine | Track the x-coordinate as an angle rotates to create y=cos x. |
| 4.3 | Amplitude, Midline & Vertical Shift | Identify and use vertical features of sinusoidal graphs. |
| 4.4 | Period & Frequency | Connect horizontal scale to repeated cycles. |
| 4.5 | Phase Shift | Interpret horizontal translations of sine and cosine. |
| 4.6 | Tangent & Cotangent | Graph periodic functions with zeros and vertical asymptotes. |
| 4.7 | Secant & Cosecant | Use reciprocal relationships to graph secant and cosecant. |
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.
From Unit Circle to Sine
Track the y-coordinate as an angle rotates to create y=sin x.
From Unit Circle to Cosine
Track the x-coordinate as an angle rotates to create y=cos x.
Amplitude, Midline & Vertical Shift
Identify and use vertical features of sinusoidal graphs.
Period & Frequency
Connect horizontal scale to repeated cycles.
Phase Shift
Interpret horizontal translations of sine and cosine.
Tangent & Cotangent
Graph periodic functions with zeros and vertical asymptotes.
Secant & Cosecant
Use reciprocal relationships to graph secant and cosecant.
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.
From Unit Circle to Sine
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →From Unit Circle to Cosine
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Amplitude, Midline & Vertical Shift
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Period & Frequency
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Phase Shift
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Tangent & Cotangent
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Secant & Cosecant
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.
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.
Read a sinusoid
Show solution
Period
Show solution
Phase shift
Show solution
Build a model
Show solution
Tangent
Show solution
Reciprocal graph
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 track the y-coordinate as an angle rotates to create y=sin x.
- I can track the x-coordinate as an angle rotates to create y=cos x.
- I can identify and use vertical features of sinusoidal graphs.
- I can connect horizontal scale to repeated cycles.
- I can interpret horizontal translations of sine and cosine.
- I can graph periodic functions with zeros and vertical asymptotes.
- I can use reciprocal relationships to graph secant and cosecant.
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
Periodic Data Model
Collect or use periodic data such as daylight, tides, seasonal temperature, Ferris-wheel height, or a rotating sensor. Build a sinusoidal model and interpret amplitude, midline, period, and phase shift in context.
Evidence to include
A labeled mathematical model, organized calculations, appropriate units and precision, a written interpretation, and a check or discussion of limitations.