Integrated Math II · Week 28 · Similarity and Right Triangle Trigonometry
The Pythagorean Identity
Proving sin² + cos² = 1 and why some truths always hold.
- Students will
- Students show that sin² + cos² = 1 using the Pythagorean theorem and use it to find a missing sine or cosine of an acute angle.
- SEL skill
- Use curiosity to ask why a rule works before relying on it
- What it looks like
- Students notice how a feeling of curiosity helps them think about why a rule works, not only that it works.
- Content focus
- The Pythagorean identity sin² + cos² = 1
- Format
- Collaborative analysis
Responsible decision-making
Responsible decision-making is making a caring and constructive choice after looking at the evidence and the possible effects. More responsible decision-making activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- F-TF.8: High School Functions: Trigonometric Functions, standard 8
- Standard for Mathematical Practice: MP7 Look for and make use of structure
- CA Mathematics Framework (2023): Discovering Shape and Space
- Traditional course: Algebra II
Fits these textbook chapters
- CCSS Integrated Pathway Mathematics II, Unit 5: Similarity, Right Triangle Trigonometry, and Proof
- CPM Core Connections Integrated II, Chapter 6: More Right Triangles
- Savvas enVision Integrated Mathematics II, Topic 9: Similarity and Right Triangles
Textbook names are used only to help you find activities that fit what you teach. RoseThread Connect is not affiliated with these publishers.
More responsible decision-making activities for Integrated Math II
- Rational or Not? Responsible decision-makingStudents argue whether sums and products are rational, practicing evidence over gut feeling.
- The Quadratic Formula Responsible decision-makingChoosing the best solving method and explaining the decision.
- Comparing Growth Responsible decision-makingExponential eventually beats linear; comparing two savings plans.
- Conditional Thinking Responsible decision-makingGiven that changes probability; how context changes the meaning of a claim.
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RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL.