Rewriting Toward the Target: Proving Trigonometric Identities
Shared by A STEM Educator
Students will prove trigonometric identities by strategically rewriting one side of an equation using Pythagorean, Sum/Difference, and Double-Angle identities, verifying equivalence both algebraically and graphically.
Lesson Overview
Students progress from recognizing Pythagorean identities as rewriting tools to constructing multi-step proofs involving Sum/Difference and Double-Angle identities, always framing each step as 'moving toward a Target State.' A guided Identify-the-Flaw activity and graphical equivalence check build structural reasoning over blind manipulation.
Materials
- Vertical whiteboard or large window surface with dry-erase markers
- Pencil and paper
- Phone calculator or graphing utility (Desmos on any device)
Scaffolded Task Progression
Target State (right side):
What single step gets you there? Name the identity you used.
Target State:
Which Pythagorean identity replaces part of the left side?
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