Pre-Calculus 30 – Trigonometry & Unit Circle

by Nicholas Ciarciaglini

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Journal Reflections – Chapter 4

Summary
Journal prompts encourage students to reflect on their understanding of trigonometry concepts throughout the chapter. Students explain reasoning, identify challenges, and connect ideas across sections. These reflections support metacognition and conceptual understanding.

Purpose

• Provide insight into student understanding
• Assessment AS Learning
• Encourage mathematical thinking

Angles and Angle Measure

Notes

Summary
These notes introduce angles in standard position and extend student understanding of angle measurement using degrees and radians. Students learn how reference angles and coterminal angles describe equivalent rotations, and how arc length connects radian measure to geometric meaning. Emphasis is placed on visual reasoning, diagrams, and understanding rotation rather than memorization.

Includes

• Angles in standard position
• Degree–radian conversions
• Reference angles
• Coterminal angles and general form
• Arc length

Student Notes (Not filled)

Trigonometry and the Unit Circle – Angles and Angle Measure (Notes)Download

Assignments

TBD (Work in Progress)

Journal

Trigonometry and The Unit Circle – Angles and Angle Measure (Journal)Download

Desmos

Conversion between Degrees and Radians

Coterminal Angles

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The Unit Circle

Notes

Summary
These notes introduce the unit circle as a geometric model for trigonometry. Students define the unit circle, determine coordinates of points on the circle, and explore patterns using multiples of π. Special angles and symmetry are emphasized to reduce memorization and strengthen conceptual understanding.

Includes

• Definition and equation of the unit circle
• Coordinates on the unit circle
• Special angles
• Multiples of π
• Visual and diagram-based reasoning

Assignments

TBD (Work in Progress)

Journals

Desmos

Unit Circle

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Trigonometric Ratios

Notes

Summary
These notes connect trigonometric ratios to coordinates on the unit circle. Sine, cosine, and tangent are defined using x- and y-coordinates, and reciprocal ratios are introduced. Students also extend their understanding to points outside the unit circle using distance from the origin.

Includes

• Definitions of sin, cos, tan
• Reciprocal trigonometric ratios
• Exact vs. approximate values
• Trigonometric ratios outside the unit circle
• Sign conventions by quadrant

Assignments

TBD (Work in Progress)

Journals

Desmos

TBD (Work in Progress)

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Introduction to Trigonometric Equations

Notes

Summary
These notes introduce trigonometric equations and focus on solving them within a given domain. Students learn how to isolate trigonometric ratios, identify when no solutions exist, and solve equations that require factoring. Emphasis is placed on understanding solution sets rather than creating equations.

Includes

• Definition of trigonometric equations
• Solving linear trigonometric equations
• No-solution cases
• Factoring trigonometric equations
• General solutions and domain restrictions

Assignments

TBD (Work in Progress)

Journals

Desmos

TBD (Work in Progress)

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Additional Resources

Desmos – Review & Practice

TBD (Work in Progress)

Reference Sheets

TBD (Work in Progress)

YouTube Videos

TBD (Work in Progress)

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