What the learner will study

• Fundamental, Reciprocal & Pythagorean Identities
• Verifying Identities with Equivalent Transformations
• Sum and Difference Identities
• Double-Angle and Half-Angle Identities
• Solving Trigonometric Equations on Intervals
• Law of Sines, Ambiguous Case & Applications
• Law of Cosines & Heron-Type Area Reasoning
• Navigation, Vectors & Multi-Step Triangle Models

How to support without taking over

• Ask the learner to define inputs, outputs, units, and domain.
• Ask which property or theorem justifies each transformation.
• Request an independent check by substitution, graph, table, or alternate method.
• Encourage correction notes rather than erasing evidence of learning.
• Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Trigonometric Proof & Navigation Defense asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.